Publications
2024
New examples of twisted Brill–Noether loci I
Brambila-Paz, L., & Newstead, P. E. (2024). New examples of twisted Brill–Noether loci I. International Journal of Mathematics, 35(09). doi:10.1142/s0129167x24410039
2023
Stability and deformations of generalised Picard sheaves
Biswas, I., Brambila-Paz, L., & Newstead, P. E. (2023). Stability and deformations of generalised Picard sheaves. MANUSCRIPTA MATHEMATICA. doi:10.1007/s00229-023-01468-5
2022
Higher rank Brill—Noether theory and coherent systems open questions
Newstead, P. E. (n.d.). Higher rank Brill—Noether theory and coherent systems open questions. Proyecciones (Antofagasta), 41(2), e5276. doi:10.22199/issn.0717-6279-5276
2021
Coherent Systems on the Projective Line
Newstead, P., & Teixidor i Bigas, M. (2021). Coherent Systems on the Projective Line. The Quarterly Journal of Mathematics, 72(1-2), 115-136. doi:10.1093/qmathj/haaa024
2020
Nonemptiness and smoothness of twisted Brill-Noether loci
Hitching, G. H., Hoff, M., & Newstead, P. E. (2020). Nonemptiness and smoothness of twisted Brill-Noether loci. Annali di Matematica Pura ed Applicata. doi:10.1007/s10231-020-01009-x
2018
SESHADRI CONSTANTS AND GRASSMANN BUNDLES OVER CURVES
Biswas, I., Hanumanthu, K., Nagaraj, D. S., & Newstead, P. E. (2020). SESHADRI CONSTANTS AND GRASSMANN BUNDLES OVER CURVES. ANNALES DE L INSTITUT FOURIER, 70(4), 1477-1496. Retrieved from https://www.webofscience.com/
Some examples of rank-2 Brill-Noether loci
Newstead, P. E. (2018). Some examples of rank-2 Brill-Noether loci. REVISTA MATEMATICA COMPLUTENSE, 31(1), 201-215. doi:10.1007/s13163-017-0241-6
2017
Generated coherent systems and a conjecture of D. C. Butler
Brambila-Paz, L., Mata-Gutierrez, O., Newstead, P. E., & Ortega, A. (2019). Generated coherent systems and a conjecture of D. C. Butler. INTERNATIONAL JOURNAL OF MATHEMATICS, 30(5). doi:10.1142/S0129167X19500241
Higher rank BN-theory for curves of genus 6
Lange, H., & Newstead, P. E. (2018). Higher rank BN-theory for curves of genus 6. INTERNATIONAL JOURNAL OF MATHEMATICS, 29(2). doi:10.1142/S0129167X18500143
2016
VBAC: A Brief History
Newstead, P. (2016). VBAC: A Brief History. In INTERNATIONAL JOURNAL OF MATHEMATICS Vol. 27. doi:10.1142/S0129167X1602002X
HIGGS BUNDLES OVER ELLIPTIC CURVES FOR REAL GROUPS
Franco, E., Garcia-Prada, O., & Newstead, P. E. (2019). HIGGS BUNDLES OVER ELLIPTIC CURVES FOR REAL GROUPS. QUARTERLY JOURNAL OF MATHEMATICS, 70(1), 105-146. doi:10.1093/qmath/hay037
2015
Higher rank BN-theory for curves of genus 5
Lange, H., & Newstead, P. E. (2016). Higher rank BN-theory for curves of genus 5. REVISTA MATEMATICA COMPLUTENSE, 29(3), 691-717. doi:10.1007/s13163-016-0203-4
Higher rank BN-theory for curves of genus 4
Lange, H., & Newstead, P. E. (2017). Higher rank BN-theory for curves of genus 4. COMMUNICATIONS IN ALGEBRA, 45(9), 3948-3966. doi:10.1080/00927872.2016.1251938
2013
Nonemptiness of Brill-Noether loci in <i>M</i>(2<i>, L</i>)
Lange, H., Newstead, P. E., & Strehl, V. (2015). Nonemptiness of Brill-Noether loci in <i>M</i>(2<i>, L</i>). INTERNATIONAL JOURNAL OF MATHEMATICS, 26(13). doi:10.1142/S0129167X15501086
HIGGS BUNDLES OVER ELLIPTIC CURVES FOR COMPLEX REDUCTIVE GROUPS
Franco, E., Garcia-Prada, O., & Newstead, P. E. (2019). HIGGS BUNDLES OVER ELLIPTIC CURVES FOR COMPLEX REDUCTIVE GROUPS. GLASGOW MATHEMATICAL JOURNAL, 61(2), 297-320. doi:10.1017/S0017089518000228
On linear series and a conjecture of D. C. Butler
Bhosle, U. N., Brambila-Paz, L., & Newstead, P. E. (2015). On linear series and a conjecture of D. C. Butler. INTERNATIONAL JOURNAL OF MATHEMATICS, 26(2). doi:10.1142/S0129167X1550007X
On coherent systems with fixed determinant
Grzegorczyk, I., & Newstead, P. E. (2014). On coherent systems with fixed determinant. INTERNATIONAL JOURNAL OF MATHEMATICS, 25(5). doi:10.1142/S0129167X14500451
Higgs bundles over elliptic curves
Franco, E., Garcia-Prada, O., & Newstead, P. E. (2013). Higgs bundles over elliptic curves. Illinois J.Math.58 (1) (2014), 43--96. Retrieved from http://arxiv.org/abs/1302.2881v1
Bundles computing Clifford indices on trigonal curves
Lange, H., & Newstead, P. E. (2013). Bundles computing Clifford indices on trigonal curves. Retrieved from http://arxiv.org/abs/1301.6474v2
2012
Bundles of rank 3 on curves of Clifford index 3
Lange, H., & Newstead, P. E. (2012). Bundles of rank 3 on curves of Clifford index 3. J. Symbolic Computation 57 (2013), 3-18. Retrieved from http://dx.doi.org/10.1016/j.jsc.2013.05.002
On bundles of rank 3 computing Clifford indices
Lange, H., & Newstead, P. E. (2012). On bundles of rank 3 computing Clifford indices. Kyoto J. Math. 53, no. 1 (2013), 25-54. Retrieved from http://dx.doi.org/10.1215/21562261-1966062
Bundles of rank 2 with small Clifford index
Newstead, P. E. (2012). Bundles of rank 2 with small Clifford index. In C. Faber, G. Farkas, & R. de Jong (Eds.), Geometry and Arithmetic (pp. 267-281). Zurich: European Mathematical Society.
Introduction to Moduli Problems and Orbit Spaces
Newstead, P. E. (2012). Introduction to Moduli Problems and Orbit Spaces (Vol. 51). Mumbai: Narosa Publishing House.
2011
Hodge-Deligne polynomials of SL(2,C)-character varieties for curves of small genus
Logares, M., Muñoz, V., & Newstead, P. E. (2011). Hodge-Deligne polynomials of SL(2,C)-character varieties for curves of small genus. Retrieved from http://arxiv.org/abs/1106.6011v4
<i>Koszul cohomology and algebraic geometry</i> (University Lecture Series 52)
Newstead, P. (2011). <i>Koszul cohomology and algebraic geometry</i> (University Lecture Series 52). Bulletin of the London Mathematical Society, 43(2), 411-414. doi:10.1112/blms/bdq134
Existence of alpha-stable coherent systems on algebraic curves
Newstead, P. E. (2011). Existence of alpha-stable coherent systems on algebraic curves. In Grassmannians, Moduli Spaces and Vector Bundles (pp. 121-140). Providence RI: American Mathematical Society.
Lower bounds for Clifford indices in rank three
LANGE, H., & NEWSTEAD, P. E. (2011). Lower bounds for Clifford indices in rank three. Mathematical Proceedings of the Cambridge Philosophical Society, 150(1), 23-33. doi:10.1017/s0305004110000502
2010
Vector bundles of rank 2 computing Clifford indices
Lange, H., & Newstead, P. E. (2010). Vector bundles of rank 2 computing Clifford indices. Comm. in Algebra 41:6 (2013), 2317-2345. Retrieved from http://dx.doi.org/10.1080/00927872.2012.658532
Further examples of stable bundles of rank 2 with 4 sections
Lange, H., & Newstead, P. E. (2010). Further examples of stable bundles of rank 2 with 4 sections. Retrieved from http://arxiv.org/abs/1011.0849v1
Stable bundles of rank 2 with 4 sections
Grzegorczyk, I., Mercat, V., & Newstead, P. E. (2010). Stable bundles of rank 2 with 4 sections. Internat. J. Math. 22, no.12 (2011), 1743-1762. Retrieved from http://dx.doi.org/10.1142/S0129167X11007434
Generation of vector bundles computing Clifford indices
Lange, H., & Newstead, P. E. (2010). Generation of vector bundles computing Clifford indices. Archiv der Mathematik, 94(6), 529-537. doi:10.1007/s00013-010-0126-0
On an example of Mukai
Lange, H., Mercat, V., & Newstead, P. E. (2010). On an example of Mukai. Glasgow Math. J. 54 (2012), 261-271. Retrieved from http://arxiv.org/abs/1003.4007v4
Vector Bundles and Complex Geometry
Garcia-Prada, O., Newstead, P. E., & others. (Eds.) (2010). Vector Bundles and Complex Geometry (Vol. 522). Providence RI: American Mathematical Society.
2009
Lower bounds for Clifford indices in rank three
Lange, H., & Newstead, P. E. (2009). Lower bounds for Clifford indices in rank three. Retrieved from http://arxiv.org/abs/0912.2618v1
Generation of vector bundles computing Clifford indices
Lange, H., & Newstead, P. E. (2009). Generation of vector bundles computing Clifford indices. Retrieved from http://arxiv.org/abs/0912.0815v2
Moduli Spaces of Coherent Systems of Small Slope on Algebraic Curves
Bradlow, S. B., García-Prada, O., Mercat, V., Muñoz, V., & Newstead, P. E. (2009). Moduli Spaces of Coherent Systems of Small Slope on Algebraic Curves. Communications in Algebra, 37(8), 2649-2678. doi:10.1080/00927870902747464
Geometric Invariant Theory
Newstead, P. E. (2009). Geometric Invariant Theory. In S. B. Bradlow, L. Brambila-Paz, & O. Garcia-Prada (Eds.), Moduli Spaces and Vectr Bundles (pp. 99-127). Cambridge: Cambridge University Press.
Moduli spaces of coherent systems of small slope
Bradlow, S. B., Garcia-Prada, O., Mercat, V., Munoz, V., & Newstead, P. E. (2009). Moduli spaces of coherent systems of small slope. Comm. in Algebra, 37(8), 2649-2978.
2008
Clifford indices for vector bundles on curves
Lange, H., & Newstead, P. E. (2008). Clifford indices for vector bundles on curves. Retrieved from http://arxiv.org/abs/0811.4680v3
Hodge polynomials and birational types of moduli spaces of coherent systems on elliptic curves
Lange, H., & Newstead, P. E. (2008). Hodge polynomials and birational types of moduli spaces of coherent systems on elliptic curves. Retrieved from http://arxiv.org/abs/0810.1425v2
COHERENT SYSTEMS OF GENUS 0 III: COMPUTATION OF FLIPS FOR k = 1
LANGE, H., & NEWSTEAD, P. E. (2008). COHERENT SYSTEMS OF GENUS 0 III: COMPUTATION OF FLIPS FOR k = 1. International Journal of Mathematics, 19(09), 1103-1119. doi:10.1142/s0129167x08005047
Stability of projective Poincare and Picard bundles
Biswas, I., Brambila-Paz, L., & Newstead, P. E. (2008). Stability of projective Poincare and Picard bundles. Bull. London Math. Soc. 2009. Retrieved from http://dx.doi.org/10.1112/blms/bdp017
2007
On coherent systems of type (n,d,n+1) on Petri curves
Bhosle, U. N., Brambila-Paz, L., & Newstead, P. E. (2007). On coherent systems of type (n,d,n+1) on Petri curves. Retrieved from http://arxiv.org/abs/0712.2215v1
Clifford's theorem for coherent systems
Lange, H., & Newstead, P. E. (2007). Clifford's theorem for coherent systems. Retrieved from http://arxiv.org/abs/0707.4046v2
Coherent systems of genus 0, III: Computation of flips for k=1
Lange, H., & Newstead, P. E. (2007). Coherent systems of genus 0, III: Computation of flips for k=1. Retrieved from http://arxiv.org/abs/0707.1466v2
ON THE GEOMETRY OF MODULI SPACES OF COHERENT SYSTEMS ON ALGEBRAIC CURVES
BRADLOW, S. B., GARCÍA-PRADA, O., MERCAT, V., MUÑOZ, V., & NEWSTEAD, P. E. (2007). ON THE GEOMETRY OF MODULI SPACES OF COHERENT SYSTEMS ON ALGEBRAIC CURVES. International Journal of Mathematics, 18(04), 411-453. doi:10.1142/s0129167x07004151
2006
Universal families on moduli spaces of principal bundles on curves
Balaji, V., Biswas, I., Nagaraj, D. S., & Newstead, P. E. (n.d.). Universal families on moduli spaces of principal bundles on curves. International Mathematics Research Notices. doi:10.1155/imrn/2006/80641
Coherent systems of genus 0 II: Existence results for k\ge3
Lange, H., & Newstead, P. E. (2006). Coherent systems of genus 0 II: Existence results for k\ge3. Retrieved from http://arxiv.org/abs/math/0601683v2
Universal Families on moduli spaces of principal bundles on curves
Balaji, V., Biswas, I., Nagaraj, D. S., & Newstead, P. E. (2006). Universal Families on moduli spaces of principal bundles on curves. Retrieved from http://arxiv.org/abs/math/0601168v1
On Clifford's theorem for rank-3 bundles
Lange, H., & Newstead, P. E. (2006). On Clifford's theorem for rank-3 bundles. REVISTA MATEMATICA IBEROAMERICANA, 22(1), 287-304. Retrieved from https://www.webofscience.com/
2005
'Algebraic Quotients. Torus Actions. The Adjoint Representation and the Adjoint Action'
Newstead, P. E. (2005). 'Algebraic Quotients. Torus Actions. The Adjoint Representation and the Adjoint Action'. Unknown Journal, 107(4), 25-27.
2004
On Poincare bundles of vector bundles on curves
Lange, H., & Newstead, P. E. (2004). On Poincare bundles of vector bundles on curves. Retrieved from http://arxiv.org/abs/math/0411573v1
Coherent Systems on Elliptic curves
Lange, H., & Newstead, P. E. (2004). Coherent Systems on Elliptic curves. Retrieved from http://arxiv.org/abs/math/0411064v3
2003
Coherent systems of genus 0
Lange, H., & Newstead, P. E. (2003). Coherent systems of genus 0. Retrieved from http://arxiv.org/abs/math/0311239v1
On Clifford's theorem for rank-3 bundles
Lange, H., & Newstead, P. E. (2003). On Clifford's theorem for rank-3 bundles. Retrieved from http://arxiv.org/abs/math/0310463v1
Coherent Systems and Brill–Noether Theory
Bradlow, S. B., García-Prada, O., Muñoz, V., & Newstead, P. E. (2003). Coherent Systems and Brill–Noether Theory. International Journal of Mathematics, 14(07), 683-733. doi:10.1142/s0129167x03002009
Deformations of the generalised Picard bundle
Biswas, I., Brambila-Paz, L., & Newstead, P. E. (2003). Deformations of the generalised Picard bundle. Retrieved from http://arxiv.org/abs/math/0308292v1
2002
Maximal Subbundles and Gromov-Witten Invariants
Lange, H., & Newstead, P. E. (2002). Maximal Subbundles and Gromov-Witten Invariants. Retrieved from http://arxiv.org/abs/math/0204216v2
2001
ON CLIFFORD'S THEOREM FOR VECTOR BUNDLES ON ALGEBRAIC CURVES
Ballico, E., & Newstead, P. E. (2001). ON CLIFFORD'S THEOREM FOR VECTOR BUNDLES ON ALGEBRAIC CURVES. Communications in Algebra, 29(8), 3223-3237. doi:10.1081/agb-100105018
2000
NONEMPTINESS OF BRILL–NOETHER LOCI
BRAMBILA-PAZ, L., MERCAT, V., NEWSTEAD, P. E., & ONGAY, F. (2000). NONEMPTINESS OF BRILL–NOETHER LOCI. International Journal of Mathematics, 11(06), 737-760. doi:10.1142/s0129167x00000350
1999
NONEMPTINESS OF BRILL-NOETHER LOCI IN <i>M</i> (2, <i>K</i>)
Lange, H., Newstead, P. E., & Park, S. S. (2016). NONEMPTINESS OF BRILL-NOETHER LOCI IN <i>M</i> (2, <i>K</i>). COMMUNICATIONS IN ALGEBRA, 44(2), 746-767. doi:10.1080/00927872.2014.990020
1998
On the cohomology ring of the moduli space of rank 2 vector bundles on a curve
King, A. D., & Newstead, P. E. (1998). On the cohomology ring of the moduli space of rank 2 vector bundles on a curve. Topology, 37(2), 407-418. doi:10.1016/s0040-9383(97)00041-4
1997
Geography of Brill-Noether loci for small slopes
Brambila-Paz, L., Grzegorczyk, I., & Newstead, P. E. (1997). Geography of Brill-Noether loci for small slopes. Journal of Algebraic Geometry, 6(4), 645-669.
Algebraic cohomology of the moduli space of rank 2 vector bundles on a curve
Balaji, V., King, A. D., & Newstead, P. E. (1997). Algebraic cohomology of the moduli space of rank 2 vector bundles on a curve. Topology, 36(2), 567-577. doi:10.1016/0040-9383(96)00007-9
Stability of the Poincaré Bundle
Balaji, V., Brambila‐Paz, L., & Newstead, P. E. (1997). Stability of the Poincaré Bundle. Mathematische Nachrichten, 188(1), 5-15. doi:10.1002/mana.19971880102
1995
Geography of Brill-Noether loci for small slopes
Paz, L. B., Grzegorczyk, I., & Newstead, P. E. (1995). Geography of Brill-Noether loci for small slopes. Retrieved from http://arxiv.org/abs/alg-geom/9511003v1
Stability of the Poincaré bundle
Balaji, V., Paz, L. B., & Newstead, P. E. (1995). Stability of the Poincaré bundle. Retrieved from http://arxiv.org/abs/alg-geom/9506011v1
1986
On the geometry of the planar 4-bar mechanism
Gibson, C. G., & Newstead, P. E. (1986). On the geometry of the planar 4-bar mechanism. Acta Applicandae Mathematicae, 7(2), 113-135. doi:10.1007/bf00051348
1985
Uniform Bundles on Quadric Surfaces and Some Related Varieties
Ballico, E., & Newstead, P. E. (1985). Uniform Bundles on Quadric Surfaces and Some Related Varieties. Journal of the London Mathematical Society, s2-31(2), 211-223. doi:10.1112/jlms/s2-31.2.211
1984
On the relations between characteristic classes of stable bundles of rank 2 over an algebraic curve
Newstead, P. E. (n.d.). On the relations between characteristic classes of stable bundles of rank 2 over an algebraic curve. Bulletin of the American Mathematical Society, 10(2), 292-294. doi:10.1090/s0273-0979-1984-15252-2
1983
A Space Curve whose Normal Bundle is Stable
Newstead, P. E. (1983). A Space Curve whose Normal Bundle is Stable. Journal of the London Mathematical Society, s2-28(3), 428-434. doi:10.1112/jlms/s2-28.3.428
On the Plane Sections of a Quadric Hypersurface
Newstead, P. E. (1983). On the Plane Sections of a Quadric Hypersurface. Bulletin of the London Mathematical Society, 15(3), 226-228. doi:10.1112/blms/15.3.226
Pencils on Conic Bundles
Newstead, P. E. (1983). Pencils on Conic Bundles. Journal of the London Mathematical Society, s2-27(1), 19-28. doi:10.1112/jlms/s2-27.1.19
1982
ON THE COHOMOLOGY AND THE PICARD GROUP OF A MODULI SPACE OF BUNDLES ON P<sup>3</sup>
NEWSTEAD, P. E. (1982). ON THE COHOMOLOGY AND THE PICARD GROUP OF A MODULI SPACE OF BUNDLES ON P<sup>3</sup>. The Quarterly Journal of Mathematics, 33(3), 349-355. doi:10.1093/qmath/33.3.349
Covariants of pencils of binary cubics
Newstead, P. E. (1982). Covariants of pencils of binary cubics. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 91(3-4), 181-183. doi:10.1017/s0308210500017431
Quadratic complexes. II
Newstead, P. E. (1982). Quadratic complexes. II. Mathematical Proceedings of the Cambridge Philosophical Society, 91(2), 183-206. doi:10.1017/s0305004100059247
1981
Comparison theorems for conic bundles
Newstead, P. E. (1981). Comparison theorems for conic bundles. Mathematical Proceedings of the Cambridge Philosophical Society, 90(1), 21-31. doi:10.1017/s0305004100058497
Invariants of pencils of binary cubics
Newstead, P. E. (1981). Invariants of pencils of binary cubics. Mathematical Proceedings of the Cambridge Philosophical Society, 89(2), 201-209. doi:10.1017/s0305004100058102
Real classification of complex conics
Newstead, P. E. (1981). Real classification of complex conics. Mathematika, 28(1), 36-53. doi:10.1112/s0025579300015333
1980
Rationality of moduli spaces of stable bundles
Newstead, P. E. (1980). Rationality of moduli spaces of stable bundles. Mathematische Annalen, 249(3), 281-282. doi:10.1007/bf01363901
The fundamental group of a moduli space of bundles on P3
Newstead, P. E. (1980). The fundamental group of a moduli space of bundles on P3. Topology, 19(4), 419-426. doi:10.1016/0040-9383(80)90024-5
1975
Rationality of moduli spaces of stable bundles
Newstead, P. E. (1975). Rationality of moduli spaces of stable bundles. Mathematische Annalen, 215(3), 251-268. doi:10.1007/bf01343893
1973
A Non-Existence Theorem for Families of Stable Bundles
Newstead, P. E. (1973). A Non-Existence Theorem for Families of Stable Bundles. Journal of the London Mathematical Society, s2-6(2), 259-266. doi:10.1112/jlms/s2-6.2.259
1972
Characteristic classes of stable bundles of rank 2 over an algebraic curve
Newstead, P. E. (n.d.). Characteristic classes of stable bundles of rank 2 over an algebraic curve. Transactions of the American Mathematical Society, 169(0), 337-345. doi:10.1090/s0002-9947-1972-0316452-9
1968
Stable bundles of rank 2 and odd degree over a curve of genus 2
Newstead, P. E. (1968). Stable bundles of rank 2 and odd degree over a curve of genus 2. Topology, 7(3), 205-215. doi:10.1016/0040-9383(68)90001-3
1967
Topological properties of some spaces of stable bundles
Newstead, P. E. (1967). Topological properties of some spaces of stable bundles. Topology, 6(2), 241-262. doi:10.1016/0040-9383(67)90037-7
1964
Reducible vector bundles on a quadric surface
Newstead, P. E., & Schwarzenberger, R. L. E. (1964). Reducible vector bundles on a quadric surface. Mathematical Proceedings of the Cambridge Philosophical Society, 60(3), 421-424. doi:10.1017/s0305004100037920