Infinite transitivity, finite generation, and demazure roots
TLDR
In this article, it was shown that if a toric variety X is smooth in codimension 2 then one can find a subgroup of SAut(X) generated by a finite number of one-parameter unipotent subgroups which has the same transitivity property.About:
This article is published in Advances in Mathematics.The article was published on 2019-07-31 and is currently open access. It has received 19 citations till now. The article focuses on the topics: Toric variety & Affine variety.read more
Citations
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On nilpotent generators of the Lie algebra sln
TL;DR: For the special linear Lie algebra sl n (K ) over an infinite field of characteristic different from 2, it was shown in this paper that for any nonzero nilpotent X there exists an X and a Y such that the matrices X and Y generate the Lie algebra SL n ( K ).
Fano-Mukai fourfolds of genus 10 as compactifications of ℂ^4
Prokhorov Yu.,Zaidenberg Mikhail +1 more
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Tits-type Alternative for Groups Acting on Toric Affine Varieties
TL;DR: In this article, it was shown that the group generated by the torus acting on a toric affine algebraic variety $X$ and a collection of one-parameter unipotent subgroups $U_1,\ldots,U_s$ of the toric variety is a non-abelian free subgroup.
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An algorithmic approach to the Polydegree Conjecture for plane polynomial automorphisms
TL;DR: In this article, the interaction between two structures on the group of polynomial automorphisms of the affine plane has been studied, and it has been shown that the Polydegree Conjecture is algorithmically decidable.
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Tits alternative and highly transitive actions on toric varieties
TL;DR: In this article, a toric affine algebraic variety (X) and a collection of one-parameter unipotent subgroups (U_1,\ldots,U_s) of the torus acting on it are compared.
References
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Book
Introduction to Toric Varieties.
TL;DR: In this article, a mini-course is presented to develop the foundations of the study of toric varieties, with examples, and describe some of these relations and applications, concluding with Stanley's theorem characterizing the number of simplicies in each dimension in a convex simplicial polytope.
Book
Kac-Moody Groups, their Flag Varieties and Representation Theory
TL;DR: In this article, Kac-Moody Lie Algebra Homology and Cohomology has been studied in the context of representation theory of kac-moody groups.
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Erratum to “The homogeneous coordinate ring of a toric variety”
TL;DR: In this paper, the authors introduce the homogeneous coordinate ring S of a toric variety X. The ring S is a polynomial ring with one variable for each one-dimensional cone in the fan ∆ determining X, and S has a natural grading determined by the monoid of effective divisor classes.
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Sous-groupes algébriques de rang maximum du groupe de Cremona
TL;DR: In this article, Gauthier-Villars implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/legal.php).
Book
Algebraic theory of locally nilpotent derivations
TL;DR: In this paper, the Makar-Limanov and Derksen invariants are used for locally non-potent derivatives of polynomial rings and linear actions of unipotent groups.