List of Publications

2023

Ivan Arzhantsev. Automorphisms of algebraic varieties and infinite transitivity. St. Petersburg Mathematical Journal 34 (2023), no. 2, 143-178

Ivan Arzhantsev. Normally located polyhedra https://arxiv.org/abs/2301.02688, 8 pages

Ivan Arzhantsev. On conjugacy of additive actions in the affine Cremona group.   https://arxiv.org/abs/2308.12096 , 6 pages

Ivan Arzhantsev. On images of affine spaces. Indagationes Mathematicae 34 (2023), no. 4, 812-819

Ivan Arzhantsev, Shulim Kaliman, and Mikhail Zaidenberg. Varieties covered by affine spaces, uniformly rational varieties and their cones. https://arxiv.org/abs/2304.08608, 13 pages

Ivan Arzhantsev and Mikhail Zaidenberg. Tits-type alternative for certain groups acting on algebraic surfaces. Proceedings of the American Mathematical Society 151 (2023), no. 7, 2813-2829

Ivan Arzhantsev and Yulia Zaitseva. Affine homogeneous varieties and suspensions. https://arxiv.org/abs/2309.06170, 11 pages

Ivan Beldiev. Gorenstein algebras and uniqueness of additive actions. Results in Mathematics 78 (2023), no. 5, article 192

Nikhilesh Dasgupta and Sergey Gaifullin. On locally nilpotent derivations of polynomial algebra in three variables. https://arxiv.org/abs/2306.00510, 29 pages

Nikhilesh Dasgupta and Animesh Lahiri. Isotropy subgroups of some almost rigid domains. Journal of Pure and Applied Algebra 227 (2023), no. 4, article 107250

Polina Evdokimova, Sergey Gaifullin and Anton Shafarevich. Rigid trinomial varieties. https://arxiv.org/pdf/2307.06672.pdf, 8 pages

Evgeny Feigin, Igor Makhlin, and Alexander Popkovich. Beyond the Sottile-Sturmfels degeneration of a semi-infinite Grassmannian. International Mathematics Research Notices IMRN 2023 (2023), no. 12, 10037–10066

Ivan Kaygorodov, Viktor Lopatkin, and Zerui Zhang. Transposed Poisson structures on Galilean and solvable Lie algebras. Journal of Geometry and Physics 187 (2023), article 104781

Veronika Kikteva. Generalization of the ABC Theorem on locally nilpotent derivations. https://arxiv.org/abs/2309.13971, 13 pages 

Alexander Perepechko and Andriy Regeta. When is the automorphism group of an affine variety nested? Transformation Groups 28 (2023), no.1, 401-412

Anton Shafarevich. Euler-symmetric projective toric varieties and additive actions. Indagationes Mathematicae 34 (2023), no. 1, 42-53

Anton Trushin. Graded automorphisms of the algebra of polynomials in three variables. Mathematical Notes 113 (2023), no. 5, 736-740

2022

Hassan Alhussein, Pavel Kolesnikov, and Viktor Lopatkin.  Morse matching method for conformal cohomologies. https://arxiv.org/abs/2204.10837, 22 pages

Ivan Arzhantsev and Roman Avdeev. Root subgroups on affine spherical varieties. Selecta Mathematica, New Series 28 (2022), no. 3, article 60

Ivan Arzhantsev and Yulia Zaitseva. Equivariant completions of affine spaces. Russian Mathematical Surveys 77 (2022), no. 4, 571–650

Ivan Arzhantsev, Yulia Zaitseva, and Kirill Shakhmatov. Homogeneous algebraic varieties and transitivity degree. Proceedings of the Steklov Institute of Mathematics 318 (2022), 13-25

Ivan Arzhantsev and Kirill Shakhmatov. Some finiteness results on triangular automorphisms. Results in Mathematics 77 (2022), no. 2, article 75

Ivan Arzhantsev, Alexander Perepechko, and Kirill Shakhmatov. Radiant toric varieties and unipotent group actions. https://arxiv.org/abs/2209.04021, 24 pages

Ivan Arzhantsev and Mikhail Zaidenberg. Tits-type alternative for groups acting on toric affine varieties. International Mathematics Research Notices IMRN 2022 (2022), no. 11, 8162–8195

Roman Avdeev and Vladimir Zhgoon. On the existence of B-root subgroups on affine spherical varieties. Doklady Mathematics 105 (2022), no. 2, 51-55

Ivan Beldiev. The Group of Isometries of K0(Pn). https://arxiv.org/abs/2212.01626, 12 pages

Boris Bilich. Classification of noncommutative monoid structures on normal affine surfaces. Proceedings of the American Mathematical Society 150 (2022), no. 10, 4129-4144

Viktoriia Borovik, Sergey Gaifullin, and Anton Trushin. Commutative actions on smooth projective quadrics. Communications in Algebra 50 (2022), no. 12, 5468-5476

Alisa Chistopolskaya. On nilpotent generators of the symplectic Lie algebra. Linear and Multilinear Algebra 70 (2022), no. 3, 490-496

Alisa Chistopolskaya and Grigory Taroyan. Infinite transitivity for automorphism group of the affine plane. https://arxiv.org/abs/2202.02214, 14 pages

Sergey Dzhunusov. On uniqueness of additive actions on complete toric varieties. Journal of Algebra 609 (2022), 642-656

Sergey Gaifullin. Orbits of the automorphism group of horospherical varieties, and divisor class group. Proceedings of the Steklov Institute of Mathematics 318 (2022), 38-44

Sergey Gaifullin and Georgiy Shirinkin. Orbits of automorphism group of trinomial hypersurfaces. https://arxiv.org/abs/2205.02513, 18 pages

Alexei Lisitsa, Viktor Lopatkin, and Alexei Vernitski. Describing realizable Gauss diagrams using the concepts of parity or bipartite graphs https://arxiv.org/abs/2212.07140, 13 pages

Viktor Lopatkin. On meandric permutations. https://arxiv.org/abs/2208.09752, 13 pages

Alexander Perepechko and Andriy Regeta. Automorphism groups of affine varieties without non-algebraic elements. https://arxiv.org/abs/2203.08950, 6 pages

Alexander Perepechko and Mikhail Zaidenberg. Automorphism groups of rigid affine surfaces: the identity component. https://arxiv.org/abs/2208.09738, 30 pages

Anton Shafarevich and Anton Trushin. On the automorphism group of a toral variety. https://arxiv.org/abs/2211.16584, 12 pages

Anton Trushin. Gradings allowing wild automorphisms. Journal of Algebra and its Applications 21 (2022), no. 8, article 2250160

2021

Ivan Arzhantsev. Limit points and additive group actions. Ricerche di Matematica. Published online (2021), 10 pages

Ivan Arzhantsev, Alvaro Liendo, and Taras Stasyuk. Lie algebras of vertical derivations on semiaffine varieties with torus actions. Journal of Pure and Applied Algebra 225 (2021), no. 2, 106499: 1-18

Ilya Boldyrev and Sergey Gaifullin. Automorphisms of Nonnormal Toric Varieties. Mathematical Notes 110 (2021), no. 6, 872-886

Victoria Borovik, Sergey Gaifullin, and Anton Shafarevich. On orbits of automorphism groups on horospherical varieties. https://arxiv.org/abs/2105.05897, 10 pages

Sergey Gaifullin. Automorphisms of Danielewski varieties. Journal of Algebra 573 (2021), 364-392

Vsevolod Gubarev and Alexander Perepechko. Injective Rota-Baxter operators of weight zero on F[x]. Mediterranean Journal of Mathematics 18 (2021), art. no. 267

Sergey Dzhunusov. Additive actions on complete toric surfaces. International Journal of Algebra and Computation 31 (2021), no. 1, 19-35

Sergey Dzhunusov and Yulia Zaitseva. Commutative algebraic monoid structures on affine surfaces. Forum Mathematicum 33 (2021), no. 1, 177-191

Abdullah Khan, Alexei Lisitsa, Viktor Lopatkin, and Alexei Vernitski. Circle graphs (chord interlacement graphs) of Gauss diagrams: Descriptions of realizable Gauss diagrams, algorithms, enumeration. https://arxiv.org/abs/2108.02873, 25 pages

Viktor Lopatkin. Garside Theory: a Composition-Diamond Lemma Point of View. https://arxiv.org/abs/2109.07595, 28 pages

Alexander Perepechko. Affine cones over cubic surfaces are flexible in codimension one. Forum Mathematicum 33 (2021), no. 2, 339-348

Alexander Perepechko. Automorphisms of surfaces of Markov type. Mathematical Notes 110 (2021), no. 5, 732-737

Anton Shafarevich. Additive actions on toric projective hypersurfaces. Results in Mathematics 76 (2021), no. 3, article 145

Kirill Shakhmatov. Smooth non-projective equivariant completions of affine spaces. Mathematical Notes 109 (2021), no. 6, 954-961

2020

Ivan Arzhantsev, Sergey Bragin, and Yulia Zaitseva. Commutative algebraic monoid structures on affine spaces. Communications in Contemporary Mathematics 22 (2020), no. 8, 1950064: 1-23

Viktoria Borovik and Sergey Gaifullin. m-suspensions over rigid varieties. https://arxiv.org/abs/2007.07882, 8 pages

Sergey Gaifullin. On rigidity of trinomial hypersurfaces and factorial trinomial varieties. https://arxiv.org/abs/1902.06136, 20 pages

2019

Ivan Arzhantsev, Karine Kuyumzhiyan, Mikhail Zaidenberg. Infinite transitivity, finite generation, and Demazure roots. Advances in Mathematics 351 (2019), 1-32

Sergey Gaifullin and Anton Shafarevich. Flexibility of normal affine horospherical varieties. Proceedings of the American Mathematical Society 147 (2019), 3317-3330

Sergey Gaifullin and Yulia Zaitseva. On homogeneous locally nilpotent derivations of trinomial algebras. Journal of Algebra and Its Applications 18 (2019), no. 10, 1950196: 1-19

Dmitry Matveev. Commuting homogeneous locally nilpotent derivations. Sbornik: Mathematics 210 (2019), no. 11, 1609-1632

Anton Shafarevich. Geometrical description of orbits of automorphism group of affine toric varieties. Moscow University Mathematical Bulletin 74 (2019), no. 5, 209-211

Yulia Zaitseva. Homogeneous locally nilpotent derivations of non-factorial trinomial algebras. Mathematical Notes 105 (2019), no. 6, 818-830

2018

Ivan Arzhantsev. Polynomial curves on trinomial hypersurfaces. Acta Arithmetica 186 (2018), no. 1, 87-99

Ivan Arzhantsev. Infinite transitivity and special automorphisms. Arkiv för Matematik 56 (2018), no. 1, 1-14

Ivan Arzhantsev. Gale duality and homogeneous toric varieties. Communications in Algebra 46 (2018), no. 8, 3539-3552

Ivan Arzhantsev, Lukas Braun, Jürgen Hausen and Milena Wrobel. Log terminal singularities, platonic tuples and iteration of Cox rings. European Journal of Mathematics 4 (2018), no. 1, 242-312

Alisa Chistopolskaya. On nilpotent generators of the special linear Lie algebra. Linear Algebra and its Applications (2018), no. 559, 73-79

Mateusz Michałek, Alexander Perepechko, and Hendrik Süß. Flexible affine cones and flexible coverings. Mathematische Zeitschrift 290 (2018), no. 3-4, 1457-1478

Nikolay Bogachev and Alexander Perepechko. Vinberg’s algorithm for hyperbolic lattices. Mathematical Notes 103 (2018), no. 5-6, 836-840

2017

Ivan Arzhantsev and Sergey Gaifullin. The automorphism group of a rigid affine variety. Mathematische Nachrichten 290 (2017), no. 5-6, 662-671

Ivan Arzhantsev and Elena Romaskevich. Additive actions on toric varieties. Proceedings of the American Mathematical Society 145 (2017), no. 5, 1865-1879

Sergei Kovalenko, Alexander Perepechko, and Mikhail Zaidenberg. On automorphism groups of affine surfaces. In: Advanced Studies in Pure Mathematics 75: Algebraic Varieties and Automorphism Groups. Mathematical Society of Japan, 2017, 207-286

Anton Shafarevich. Flexibility of affine horospherical varieties of semisimple groups. Sbornik: Mathematics 208 (2017), no. 2, 285-310

2016

Ivan Arzhantsev. On rigidity of factorial trinomial hypersurfaces. International Journal of Algebra and Computation 26 (2016), no. 5, 1061-1070

2015

Ivan Arzhantsev, Ulrich Derenthal, Jürgen Hausen, and Antonio Laface. Cox rings. Cambridge Studies in Advanced Mathematics, no. 144, Cambridge University Press, 2015, 530 pages

Ivan Arzhantsev and Polina Kotenkova. Equivariant embeddings of commutative linear algebraic groups of corank one. Documenta Mathematica 20 (2015), 1039-1053

2014

Ivan Arzhantsev and Andrey Popovskiy. Additive actions on projective hypersurfaces. In: Automorphisms in Birational and Affine Geometry, Levico Terme, Italy, October 2012, Springer Proceedings in Mathematics & Statistics 79, Springer, 2014, 17-33

Ivan Arzhantsev, Alexander Perepechko, and Hendrik Süß. Infinite transitivity on universal torsors. Journal of the London Mathematical Society 89 (2014), no. 3, 762-778

Ivan Arzhantsev, Jürgen Hausen, Elaine Herppich, and Alvaro Liendo. The automorphism group of a variety with torus action of complexity one. Moscow Mathematical Journal 14 (2014), no. 3, 429-471

Kevin Langlois and Alexander Perepechko. Demazure roots and spherical varieties: the example of horizontal SL(2)-actions. https://arxiv.org/abs/1406.5744, 41 pages

Alexander Perepechko. On solvability of the automorphism group of a finite-dimensional algebra. Journal of Algebra 403 (2014), 445-458

2013

Ivan Arzhantsev and Mikhail Zaidenberg. Acyclic curves and group actions on affine toric surfaces. In: Affine Algebraic Geometry, Proceedings of the Conference, Osaka, Japan, 3-6 March 2011, World Scientific, 2013, 1-41

Ivan Arzhantsev, Devrim Celik, and Jürgen Hausen. Factorial algebraic group actions and categorical quotients. Journal of Algebra 387 (2013), 87-98

Ivan Arzhantsev, Hubert Flenner, Shulim Kaliman, Frank Kutzschebauch, and Mikhail Zaidenberg. Flexible varieties and automorphism groups. Duke Mathematical Journal 162 (2013), no. 4, 767-823

Ivan Arzhantsev, Hubert Flenner, Shulim Kaliman, Frank Kutzschebauch, and Mikhail Zaidenberg. Infinite transitivity on affine varieties. In: Birational geometry, rational curves, and arithmetic, Birkhäuser, 2013, 1-13

Ivan Arzhantsev and Ivan Bazhov. On orbits of the automorphism group on an affine toric variety. Central European Journal of Mathematics 11 (2013), no. 10, 1713-1724

Alexander Perepechko. Flexibility of affine cones over del Pezzo surfaces of degree 4 and 5. Functional Analysis and Its Applications 47 (2013), no. 4, 45-52