?
Compressible finite groups of birational automorphisms
Doklady Mathematics. 2018. Vol. 98. No. 2. P. 413-415.
The compressibility of certain types of finite groups of birational automorphisms of algebraic varieties is established.
Vladimir L. Popov, European Journal of Mathematics 2016 Vol. 2 No. 1 P. 283-290
According to the classical theorem, every algebraic variety
endowed with a nontrivial rational action of a connected linear algebraic
group is birationally isomorphic to a product of another algebraic variety
and the projective space of a positive dimension. We show that the classical proof of this theorem
actually works only in characteristic 0 and we give a characteristic free
proof ...
Added: February 2, 2016
Popov V., / Bielefeld University. Series LAGRS "Linear Algebraic Groups and Related Structures". 2012. No. 485.
We construct counterexamples to the rationality conjecture regar-ding the new version of the Makar-Limanov invariant introduced in A. Liendo, Ga-actions of fiber type on affine T-varieties, J. Algebra 324 (2010), 3653–3665. ...
Added: January 9, 2013
Vladimir L. Popov, Transformation Groups 2014 Vol. 19 No. 2 P. 549-568
We explore orbits, rational invariant functions, and quotients of the natural actions of connected, not necessarily finite dimensional subgroups of the automorphism groups of irreducible algebraic varieties. The applications of the results obtained are given. ...
Added: March 17, 2014
Vladimir L. Popov, / Cornell University. Series math "arxiv.org". 2021. No. 2105.12861.
Starting with exploration of the possibility to present the underlying variety of an affine algebraic group in the form of a product of some algebraic varieties, we then explore the naturally arising problem as to what extent the group variety of an algebraic group determines its group structure. ...
Added: May 28, 2021
Vladimir L. Popov, / Cornell University. Series math "arxiv.org". 2015. No. 1502.02167.
According to the classical theorem, every irreducible algebraic variety endowed with a nontrivial rational action of a connected linear algebraic group is birationally isomorphic to a product of another algebraic variety and the s-dimensional projectice space with positive s. We show that the classical proof of this theorem actually works only in characteristic 0 and ...
Added: February 10, 2015
Vladimir L. Popov, Journal of the Ramanujan Mathematical Society 2013 Vol. 28A No. Special Issue-2013 dedicated to C.S.Seshadri's 80th birthday P. 409-415
We construct counterexamples to the rationality conjecture regarding the new version of the Makar-Limanov invariant formulated in A. Liendo, G_a-actions of fiber type on affine T-varieties, J. Algebra 324 (2010), 3653--3665. ...
Added: June 20, 2013
Amerik E., Campana F., / Cornell University library. Series arxiv.org "algebraic geometry". 2013.
This is a note on Beauville's problem (solved by Greb, Lehn and Rollenske in the non-algebraic case and by Hwang and Weiss in general) whether a lagrangian torus on an irreducible holomorphic symplectic manifold is a fiber of a lagrangian fibration. We provide a different, very short solution in the non-algebraic case and make some ...
Added: April 9, 2013
Athens : The Hellenic Open University, 2013
The book contains the reports of the member of the congress from the different countres. They consider the idea of the symmety in the science and in the art. ...
Added: January 30, 2014
Tokyo : American Mathematical Society, World Scientific, 2017
Preface
The workshop “Algebraic Varieties and Automorphism Groups” was held at the Research Institute of Mathematical Sciences (RIMS), Kyoto University during July 7-11, 2014. There were over eighty participants including twenty people from overseas Canada, France, Germany, India, Korea, Poland, Russia, Singapore, Switzerland, and USA.
Recently, there have been remarkable developments in algebraic geometry and related fields, ...
Added: July 12, 2017
Vladimir L. Popov, / Cornell University. Series math "arxiv.org". 2021. No. 2106.02072.
For each integer n>0, we construct a series of irreducible algebraic varieties X, for which the automorphism group Aut(X) contains as a subgroup the automorphism group Aut(F_n) of a free group F_n of rank n. For n > 1, such groups Aut(X) are nonamenable, and for n > 2, they are nonlinear and contain the ...
Added: June 7, 2021
Rumynin D., Taylor J., Linear Algebra and its Applications 2021 Vol. 610 P. 135-168
We use the structure of finite-dimensional graded algebras to develop the theory of antilinear representations of finite C_2-graded groups. A finite C_2-graded group is a finite group with a subgroup of index 2. In this theory the subgroup acts linearly, while the other coset acts antilinearly. We introduce antilinear blocks, whose structure is a crucial ...
Added: September 7, 2021
Vladimir L. Popov, / Cornell University. Series math "arxiv.org". 2023. No. 2302.13364.
We prove that for every positive integer d, there are no nonzero regular differential d-forms on every smooth irreducible projective algebraic variety birationally isomorphic to the variety of flexes of plane cubics. ...
Added: February 28, 2023
Vladimir L. Popov, / Cornell University. Series math "arxiv.org". 2022. No. 2207.08912.
Considering a certain construction of algebraic varieties X endowed with an algebraic action of the group Aut(Fn), n < ∞, we obtain a criterion for the faithfulness of this action. It gives an infinite family F of X’s such that Aut(Fn) embeds intoAut(X). For n > 3, this implies nonlinearity, and for n > 2, ...
Added: July 20, 2022
Shramov K., / Cornell University. Series arXiv "math". 2020.
We classify finite groups that can act by automorphisms and birational automorphisms on non-trivial Severi-Brauer surfaces over fields of characteristic zero. ...
Added: August 19, 2020
Shramov K., / Cornell University. Series arXiv "math". 2019.
We show that automorphism groups of Hopf and Kodaira surfaces have unbounded finite subgroups. For elliptic fibrations on Hopf, Kodaira, bielliptic, and K3 surfaces, we make some observations on finite groups acting along the fibers and on the base of such a fibration. ...
Added: November 19, 2019
V. L. Popov, Izvestiya: Mathematics, England 2019 Vol. 83 No. 4 P. 830-859
The first group of results of this paper concerns the compressibility of finite subgroups of the Cremona groups. The second concerns the embeddability of other groups in the Cremona groups and, conversely, the Cremona groups in
other groups. The third concerns the connectedness of the Cremona groups. ...
Added: September 29, 2019
Arzhantsev I., Celik D., Hausen J., Journal of Algebra 2013 Vol. 387 P. 87-98
Given an action of an affine algebraic group with only trivial characters on a factorial variety, we ask for categorical quotients. We characterize existence in the category of algebraic varieties. Moreover, allowing constructible sets as quotients, we obtain a more general existence result, which, for example, settles the case of afinitely generated algebra of invariants. ...
Added: November 13, 2013
Ю. Г. Прохоров, Известия РАН. Серия математическая 2013 Т. 77 № 3 С. 199-222
We study elements $\tau$ of order two in the birational automorphism groups of rationally connected three-dimensional algebraic varieties such that there exists a non-uniruled divisorial component of the $\tau$-fixed point locus. Using the equivariant minimal model program, we give a rough classification of such elements. ...
Added: July 1, 2013
Попов В. Л., Известия РАН. Серия математическая 2019 Т. 84 № 4 С. 194-225
The rst group of results of this paper concerns the compressibility of finite subgroups of the Cremona groups. The second concerns the embeddability of other groups in the Cremona groups and, conversely, the Cremona groups in
other groups. The third concerns the connectedness of the Cremona groups. ...
Added: July 31, 2019
Arzhantsev I., Liendo A., Stasyuk T., Journal of Pure and Applied Algebra 2021 Vol. 225 No. 2 P. 106499
Let X be a normal variety endowed with an algebraic torus action. An additive group action alpha on X is called vertical if a general orbit of alpha is contained in the closure of an orbit of the torus action and the image of the torus normalizes the image of alpha in Aut(X). Our first result in this paper ...
Added: July 29, 2020
Karzhemanov I., Zhdanovskiy I., European Journal of Mathematics 2018 Vol. 4 No. 1 P. 326-329
We consider the so-called surjective rational maps. We study how the surjectivity property behaves in families of rational maps. Some (counter) examples are provided and a general result is proved. ...
Added: March 29, 2018
Shramov K., European Journal of Mathematics 2021 Vol. 7 P. 591-612
We classify finite groups that can act by automorphisms and birational automorphisms on non-trivial Severi–Brauer surfaces over fields of characteristic zero. ...
Added: September 8, 2021
Prokhorov Y., / Cornell University. Series arXiv "math". 2021.
We survey new results on finite groups of birational transformations of algebraic varieties. ...
Added: November 25, 2021
Zürich : European Mathematical Society Publishing house, 2010
Fascinating and surprising developments are taking place in the classification of algebraic varieties. Work of Hacon and McKernan and many others is causing a wave of breakthroughs in the Minimal Model Program: we now know that for a smooth projective variety the canonical ring is finitely generated. These new results and methods are reshaping the ...
Added: October 11, 2013