Publications
2024
Birationally rigid Fano-Mori fibre spaces
Pukhlikov, A. (2024). Birationally rigid Fano-Mori fibre spaces. Forum of Mathematics, Sigma, 12(e84), 1-63. doi:10.1017/fms.2024.84
Birationally rigid hypersurfaces with quadratic singularities of low rank
Pukhlikov, A. V. (2024). Бирационально жесткие гиперповерхности с квадратичными особенностями малого ранга. Математический сборник, 215(6), 111-130. doi:10.4213/sm10061
2023
Planar Sections of a Surface Close to an Umbilic
Giblin, P., & Pukhlikov, A. (2023). Planar Sections of a Surface Close to an Umbilic. Arnold Mathematical Journal, 9(4), 481-503. doi:10.1007/s40598-022-00222-1
2022
Birational geometry of varieties fibred into complete intersections of codimension two
Pukhlikov, A. V. (2022). Birational geometry of varieties fibred into complete intersections of codimension two. IZVESTIYA MATHEMATICS, 86(2), 334-411. doi:10.1070/IM9146
Effective results in the theory of birational rigidity
Pukhlikov, A. V. (2022). Effective results in the theory of birational rigidity. RUSSIAN MATHEMATICAL SURVEYS, 77(2), 301-354. doi:10.1070/RM10039
2021
Remarks on Galois Rational Coverings
Pukhlikov, A. V. (2021). Remarks on Galois Rational Coverings. MATHEMATICAL NOTES, 110(1-2), 242-247. doi:10.1134/S0001434621070257
Birational geometry of singular Fano double spaces of index two
Pukhlikov, A. V. (2021). Birational geometry of singular Fano double spaces of index two. SBORNIK MATHEMATICS, 212(4), 551-566. doi:10.1070/SM9363
2020
Birational geometry of singular Fano hypersurfaces of index two
Pukhlikov, A. V. (2020). Birational geometry of singular Fano hypersurfaces of index two. Manuscripta Mathematica, 161(1-2), 161-203. doi:10.1007/s00229-018-1075-3
Rationally connected rational double covers of primitive Fano varieties
Pukhlikov, A. V. (n.d.). Rationally connected rational double covers of primitive Fano varieties. Épijournal de Géométrie Algébrique, 4. doi:10.46298/epiga.2020.volume4.5890
2019
Canonical and log canonical thresholds of multiple projective spaces
Pukhlikov, A. V. (2019). Canonical and log canonical thresholds of multiple projective spaces. European Journal of Mathematics. doi:10.1007/s40879-019-00388-7
Birationally rigid complete intersections of high codimension
Evans, D., & Pukhlikov, A. V. (2019). Birationally rigid complete intersections of high codimension. IZVESTIYA MATHEMATICS, 83(4), 743-769. doi:10.1070/IM8782
Canonical and log canonical thresholds of multiple projective spaces
Pukhlikov, A. V. (n.d.). Canonical and log canonical thresholds of multiple projective spaces. Retrieved from http://arxiv.org/abs/1906.11802v1
Birationally rigid finite covers of the projective space
Pukhlikov, A. V. (2019). Birationally Rigid Finite Covers of the Projective Space. PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 307(1), 232-244. doi:10.1134/S0081543819060142
2018
Effective Birational Rigidity of Fano Double Hypersurfaces
Eckl, T., & Pukhlikov, A. (2018). Effective Birational Rigidity of Fano Double Hypersurfaces. Arnold Mathematical Journal, 4(3-4), 505-521. doi:10.1007/s40598-019-00106-x
2017
Birationally rigid complete intersections with a singular point of high multiplicity
Pukhlikov, A. V. (2019). BIRATIONALLY RIGID COMPLETE INTERSECTIONS WITH A SINGULAR POINT OF HIGH MULTIPLICITY. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 62(1), 221-239. doi:10.1017/S0013091518000184
Automorphisms of certain affine complements in the projective space
Pukhlikov, A. V. (2018). Automorphisms of certain affine complements in projective space. SBORNIK MATHEMATICS, 209(2), 276-289. doi:10.1070/SM8839
Canonical and log canonical thresholds of Fano complete intersections
Pukhlikov, A. V. (2018). Canonical and log canonical thresholds of Fano complete intersections. EUROPEAN JOURNAL OF MATHEMATICS, 4(1), 381-398. doi:10.1007/s40879-017-0152-6
BIRATIONALLY RIGID COMPLETE INTERSECTIONS OF CODIMENSION TWO
Evans, D., & Pukhlikov, A. (2017). BIRATIONALLY RIGID COMPLETE INTERSECTIONS OF CODIMENSION TWO. BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 54(5), 1627-1654. doi:10.4134/BKMS.b160683
2016
Birational geometry of Fano hypersurfaces of index two
Pukhlikov, A. V. (2016). Birational geometry of Fano hypersurfaces of index two. Mathematische Annalen, 366(1-2), 721-782. doi:10.1007/s00208-015-1345-2
Factorial hypersurfaces
Pukhlikov, A. V. (2017). Factorial Hypersurfaces. PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 299(1), 205-218. doi:10.1134/S0081543817080144
The $4n^2$-inequality for complete intersection singularities
Pukhlikov, A. V. (2016). The $4n^2$-inequality for complete intersection singularities. Retrieved from http://dx.doi.org/10.1007/s40598-016-0060-8
On the global log canonical threshold of Fano complete intersections
Eckl, T., & Pukhlikov, A. (2016). On the global log canonical threshold of Fano complete intersections. EUROPEAN JOURNAL OF MATHEMATICS, 2(1), 291-303. doi:10.1007/s40879-015-0060-6
The Gabrielov–Khovanskii Problem for Polynomials
Pukhlikov, A. V. (2016). The Gabrielov–Khovanskii Problem for Polynomials. Arnold Mathematical Journal, 2(1), 29-68. doi:10.1007/s40598-015-0031-5
2015
Birational geometry of algebraic varieties, fibred into Fano double spaces
Pukhlikov, A. V. (2017). Birational geometry of algebraic varieties fibred into Fano double spaces. IZVESTIYA MATHEMATICS, 81(3), 618-644. doi:10.1070/IM8493
Birationally rigid Fano fibre spaces. II
Pukhlikov, A. (2015). Birationally rigid Fano fibre spaces. II. Izvestiya: Mathematics, 79(4), 809-837. doi:10.1070/IM2015v079n04ABEH002762
Birationally rigid Fano fibre spaces II
Pukhlikov, A. (2015). Birationally rigid Fano fibre spaces II. Izvestiya: Mathematics, 79(4), 809-837. doi:10.1070/IM2015v079n04ABEH0002762
Two inequalities for a sequence of blow-ups
Pukhlikov, A. V. (2015). Two inequalities for a sequence of blow-ups. MATHEMATICAL NOTES, 97(5-6), 970-973. doi:10.1134/S0001434615050351
Birational Geometry of Higher-Dimensional Fano Varieties
Pukhlikov, A. V. (2015). Birational Geometry of Higher-Dimensional Fano Varieties. PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 288, S1-S150. doi:10.1134/S0081543815030013
2014
Birationally rigid Fano complete intersections. II
Pukhlikov, A. V. (2014). Birationally rigid Fano complete intersections. II. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 688, 209-218. doi:10.1515/crelle-2012-0059
On the locus of non-rigid hypersurfaces
Eckl, T., & Pukhlikov, A. V. (2014). On the locus of non-rigid hypersurfaces. In Springer Proceedings in Mathematics and Statistics Vol. 79 (pp. 121-139). Levico Terme, Italy: Springer. doi:10.1007/978-3-319-05681-4_7
2013
Birationally rigid complete intersections of quadrics and cubics
Pukhlikov, A. V. (2013). Birationally rigid complete intersections of quadrics and cubics. Izvestiya: Mathematics, 77(4), 795-845. doi:10.1070/IM2013v077n04ABEH002661
Birational rigidity of Fano complete intersections
Pukhlikov, A. V. (2013). Birational rigidity of Fano complete intersections. Doklady Mathematics, 87(1), 34-35. doi:10.1134/s1064562413010134
2012
K-trivial structures on Fano complete intersections
Pukhlikov, A. V. (2012). K-trivial structures on Fano complete intersections. Mathematical Notes, 91(3-4), 568-574. doi:10.1134/s0001434612030315
On the multiplicity of solutions of a system of algebraic equations
Pukhlikov, A. V. (2012). On the multiplicity of solutions of a system of algebraic equations. Proceedings of the Steklov Institute of Mathematics, 276(1), 234-249. doi:10.1134/s0081543812010208
2011
Birationally rigid Fano complete intersections. II
Pukhlikov, A. V. (2011). Birationally rigid Fano complete intersections. II. arXiv:math.AG, 10 pages.
2010
Birationally rigid varieties. II. Fano fibre spaces
Pukhlikov, A. V. (2010). Birationally rigid varieties. II. Fano fibre spaces. Russian Mathematical Surveys, 65(6), 1083-1171. doi:10.1070/rm2010v065n06abeh004716
Birational geometry of Fano double spaces of index two
Pukhlikov, A. (2010). Birational geometry of Fano double spaces of index two. Izvestiya: Mathematics, 74(5), 925-991. doi:10.1070/IM2010v074n05ABEH002512
On the self-intersection of a movable linear system
Pukhlikov, A. V. (2010). On the self-intersection of a movable linear system. Journal of Mathematical Sciences, 164(1), 119-130. doi:10.1007/s10958-009-9741-3
The Rationality Problem and Birational Rigidity
Pukhlikov, A. V. (2010). The Rationality Problem and Birational Rigidity. In Cohomological and Geometric Approaches to Rationality Problems (pp. 275-311). Birkhäuser Boston. doi:10.1007/978-0-8176-4934-0_11
2009
Singularities of algebraic subvarieties and problems of birational geometry
Pukhlikov, A. V. (2009). Singularities of algebraic subvarieties and problems of birational geometry. Proceedings of the Steklov Institute of Mathematics, 267(1), 235-247. doi:10.1134/s0081543809040191
Birational geometry of singular Fano varieties
Pukhlikov, A. V. (2009). Birational geometry of singular Fano varieties. Proceedings of the Steklov Institute of Mathematics, 264(1), 159-177. doi:10.1134/s0081543809010180
Birational Geometry of Algebraic Varieties with a Pencil of Fano Cyclic Covers
Pukhlikov, A. V. (2009). Birational Geometry of Algebraic Varieties with a Pencil of Fano Cyclic Covers. Pure and Applied Mathematics Quarterly, 5(2), 641-700. doi:10.4310/pamq.2009.v5.n2.a4
2008
Birational geometry of Fano double covers
Pukhlikov, A. V. (2008). Birational geometry of Fano double covers. Sbornik: Mathematics, 199(8), 1225-1250. doi:10.1070/sm2008v199n08abeh003960
2007
Birationally rigid varieties. I. Fano varieties
Pukhlikov, A. V. (2007). Birationally rigid varieties. I. Fano varieties. Russian Mathematical Surveys, 62(5).
Explicit examples of birationally rigid Fano varieties
Pukhlikov, A. V. (2007). Explicit examples of birationally rigid Fano varieties. Moscow Mathematical Journal, 7(3), 543-560.
Fano direct products as rationally connected fibrations
Pukhlikov, A. V. (2007). Fano direct products as rationally connected fibrations. Journal of Mathematical Sciences, 140(2), 303-320. doi:10.1007/s10958-007-0425-6
Quadratic methods in optimal control theory and systems theory
Pukhlikov, A. V. (2007). Quadratic methods in optimal control theory and systems theory. In S. K. Korovin, & S. V. Emel'yanov (Eds.), Non-Linear Dynamics and Control (Vol. 5, pp. 69-98). Moscow: FIZMATLIT.
2005
Geometry of Discontinuous Systems near a Manifold of Singularities of Third Order
Pukhlikov, A. V. (2005). Geometry of Discontinuous Systems near a Manifold of Singularities of Third Order. Differential Equations, 41(12), 1710-1716. doi:10.1007/s10625-006-0007-2
Birational geometry of algebraic varieties with a pencil of Fano complete intersections
Pukhlikov, A. V. (2005). Birational geometry of algebraic varieties with a pencil of Fano complete intersections. Retrieved from http://arxiv.org/abs/math/0511090v1
Birationally rigid varieties with a pencil of Fano double covers. III
Pukhlikov, A. V. (2005). Birationally rigid varieties with a pencil of Fano double covers. III. Retrieved from http://dx.doi.org/10.1070/SM2006v197n03ABEH003761
Birationally rigid direct Fano products
Pukhlikov, A. V. (2005). Birationally rigid direct Fano products. Doklady: Mathematics, 401(2), 163-165.
2004
Birationally rigid Fano cyclic covers
Pukhlikov, A. V. (2004). Birationally rigid Fano cyclic covers. Retrieved from http://arxiv.org/abs/math/0411198v1
Birationally rigid varieties with a pencil of double Fano covers. I
Pukhlikov, A. V. (2004). Birationally rigid varieties with a pencil of double Fano covers. I. Sbornik: Mathematics, 195(7), 1039-1071. doi:10.1070/sm2004v195n07abeh000837
Birational geometry of Fano direct products
Pukhlikov, A. V. (2004). Birational geometry of Fano direct products. Retrieved from http://dx.doi.org/10.1070/IM2005v069n06ABEH002300
Birationally rigid varieties with a pencil of Fano double covers. II
Pukhlikov, A. V. (2004). Birationally rigid varieties with a pencil of Fano double covers. II. Retrieved from http://dx.doi.org/10.1070/SM2004v195n11ABEH000861
2003
Birationally rigid Fano varieties
Pukhlikov, A. V. (2003). Birationally rigid Fano varieties. Retrieved from http://arxiv.org/abs/math/0310267v1
Birationally rigid iterated Fano double covers
Pukhlikov, A. V. (2003). Birationally rigid iterated Fano double covers. Izvestiya: Mathematics. 67 (2003), no. 3, 555-596. Retrieved from http://dx.doi.org/10.1070/IM2003v067n03ABEH000438
Birationally rigid varieties with a pencil of Fano double covers. I
Pukhlikov, A. V. (2003). Birationally rigid varieties with a pencil of Fano double covers. I. Retrieved from http://arxiv.org/abs/math/0310270v1
2002
Birationally rigid Fano hypersurfaces
Pukhlikov, A. V. (2002). Birationally rigid Fano hypersurfaces. Retrieved from http://dx.doi.org/10.1070/IM2002v066n06ABEH000413
2001
Birationally rigid Fano hypersurfaces with isolated singularities
Pukhlikov, A. V. (2001). Birationally rigid Fano hypersurfaces with isolated singularities. Retrieved from http://dx.doi.org/10.1070/SM2002v193n03ABEH000640
Pukhlikov, A. V. (2001). Unknown Title. Differential Equations, 37(3), 377-400. doi:10.1023/a:1019246616381
Birationally rigid Fano complete intersections
Pukhlikov, A. V. (2001). Birationally rigid Fano complete intersections. Journal für die reine und angewandte Mathematik (Crelles Journal), 2001(541). doi:10.1515/crll.2001.095
1998
Essentials of the method of maximal singularities
Pukhlikov, A. V. (1998). Essentials of the method of maximal singularities. Retrieved from http://arxiv.org/abs/math/9806138v1
1996
Birational automorphisms of algebraic varieties with a pencil of cubic surfaces
Pukhlikov, A. V. (1996). Birational automorphisms of algebraic varieties with a pencil of cubic surfaces. Retrieved from http://arxiv.org/abs/alg-geom/9611009v1