List of Publications

2025

Viktoriia   Borovik  and   Sergey   Gaifullin. Isolated torus invariants and automorphisms groups of rigid varieties. Journal of Algebra 666 (2025), 821-839
Anton Shafarevich. Toric varieties admitting an action of a unipotent group with a finite number of orbits. Research in the Mathematical Sciences 12 (2025), no. 1, article 6

Ivan Arzhantsev. Limit points and additive group actions. Ricerche di Matematica 73 (2024), no. 2, 715-724
Ivan Arzhantsev. Algebraic groups generated by semisimple elements. https://arxiv.org/abs/2412.10936 , 6 pages
Ivan Arzhantsev. Affine cones as images of affine spaces. https://arxiv.org/abs/2407.18580 , 7 pages
Ivan Arzhantsev. On conjugacy of additive actions in the affine Cremona group. Quaestiones Mathematicae 47 (2024), no. 9, 1767-1774
Ivan Arzhantsev. Uniqueness of addition in Lie algebras revisited. https://arxiv.org/abs/2401.06241 , 13 pages
Ivan Arzhantsev, Roman Avdeev, and Yulia Zaitseva. Algebraic monoid structures on the affine 3-space. https://arxiv.org/abs/2412.09559, 14 pages
Ivan Arzhantsev, Ivan Beldiev, and Yulia Zaitseva. On normality of projective hypersurfaces with an additive action. https://arxiv.org/abs/2404.18484, 17 pages
Ivan Arzhantsev, Sergey Gaifullin, and Viktor Lopatkin. On finite-dimensional homogeneous Lie algebras of derivations of polynomial rings. https://arxiv.org/abs/2408.05627, 14 pages
Ivan Arzhantsev, Shulim Kaliman, and Mikhail Zaidenberg. Varieties covered by affine spaces, uniformly rational varieties and their cones. Advances in Mathematics 437 (2024), article 109449
Ivan Arzhantsev, Alexander Perepechko, and Kirill Shakhmatov. Radiant toric varieties and unipotent group actions. Bulletin des Sciences Mathematiques 192 (2024), article 103419
Ivan Arzhantsev and Yulia Zaitseva. Affine homogeneous varieties and suspensions. Research in the Mathematical Sciences 11 (2024), no. 2, article 27
Ivan Beldiev. The Group of Isometries of K_0(P^n). Mathematical Notes 115 (2024), no. 4, 506-519
Ivan Beldiev. On Picard number and dimension of algebraic homogeneous spaces. https://arxiv.org/abs/2412.07044 , 14 pages
Ilya Boldyrev. Makar-Limanov invariants of nonnormal affine toric varieties. Mediterranean Journal of Mathematics 21 (2024), no. 3, article 93
Victoria Borovik, Sergey Gaifullin, and Anton Shafarevich. On orbits of automorphism groups on horospherical varieties. Mathematische Nachrichten 297 (2024), no. 9, 3174-3183
Viktoriia Borovik, Alexander Chernov, and Anton Shafarevich. Additive actions on projective hypersurfaces with a finite number of orbits. https://arxiv.org/abs/2405.00171, 9 pages
Sergey Gaifullin and Anton Shafarevich. Modified Makar-Limanov and Derksen invariants. Journal of Pure and Applied Algebra 228 (2024), no. 6, article 107616
Veronika Kikteva. On the connectedness of the automorphism group of an affine toric variety. https://arxiv.org/abs/2409.10349 , 20 pages
Ekaterina Presnova and Evgeny Smirnov. Lascoux polynomials and subdivisions of Gelfand-Zetlin polytopes. International Mathematics Research Notices IMRN 2024 (2024), no. 19, 12954–12977
Alexander Perepechko and Andriy Regeta. Automorphism groups of affine varieties consisting of algebraic elements. Proceedings of the American Mathematical Society 152 (2024), no. 6, 2377-2383
Anton Trushin. Automorphisms of rigid hypersurfaces with separable variables. https://arxiv.org/abs/2407.09235 , 5 pages
Yulia Zaitseva. Affine monoids of corank one. Results in Mathematics 79 (2024), no. 7, article 249  

2023

Roman Avdeev and Vladimir Zhgoon. On B-root subgroups on horospherical varieties. https://arxiv.org/abs/2312.03377, 13 pages 
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 images of affine spaces. Indagationes Mathematicae 34 (2023), no. 4, 812-819
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 Beldiev. Gorenstein algebras and uniqueness of additive actions. Results in Mathematics 78 (2023), no. 5, article 192
Ilya Boldyrev, Sergey Gaifullin, and Anton Shafarevich. Modified Derksen invariant. https://arxiv.org/abs/2312.08421, 12 pages
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
Sergey Gaifullin and Dmitriy Chunaev. Varieties with a torus action of complexity one having a finite number of automorphism group orbits. https://arxiv.org/abs/2311.02481, 7 pages
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. Siberian Mathematical Journal 64 (2023), no. 5, 1167-1178
Alexei Lisitsa, Viktor Lopatkin, and Alexei Vernitski. Describing realizable Gauss diagrams using the concepts of parity or bipartite graphs. Journal of Knot Theory and Its Ramifications 32 (2023), no. 10, article 2350059
Alexander Perepechko. Generic flexibility of affine cones over del Pezzo surfaces in Sagemath. https://arxiv.org/abs/2305.06462, 10 pages
Alexander Perepechko. Structure of connected nested automorphism groups. https://arxiv.org/abs/2312.08359, 9 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 Shafarevich and Anton Trushin. On the automorphism group of a toral variety. Mathematical Communications 28 (2023), no. 2, 277-291
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 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
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
Viktor Lopatkin. On meandric permutations. https://arxiv.org/abs/2208.09752, 13 pages
Alexander Perepechko and Mikhail Zaidenberg. Automorphism groups of rigid affine surfaces: the identity component. https://arxiv.org/abs/2208.09738, 30 pages
Anton Trushin. Gradings allowing wild automorphisms. Journal of Algebra and its Applications 21 (2022), no. 8, article 2250160

2021

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
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
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
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