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pro vyhledávání: '"Perepechko, Alexander"'
Autor:
Perepechko, Alexander
A nested group is an increasing union of algebraic groups. It is well known that any algebraic subgroup of the automorphism group $\mathrm{Aut}(X)$ of an affine variety $X$ is closed with respect to the ind-topology. The closedness of connected neste
Externí odkaz:
http://arxiv.org/abs/2312.08359
Autor:
Perepechko, Alexander
Generic flexibility of affine cones over del Pezzo surfaces are subject of active study recently. The question is completely studied in degree at least 3, and partially in degree 2. We present a Sagemath module that facilitates most operations for ve
Externí odkaz:
http://arxiv.org/abs/2305.06462
Publikováno v:
Bulletin des Sciences Math\'ematiques 192 (2024), 103419
We consider complete toric varieties $X$ such that a maximal unipotent subgroup $U$ of the automorphism group $\text{Aut}(X)$ acts on $X$ with an open orbit. It turns out that such varieties can be characterized by several remarkable properties. We s
Externí odkaz:
http://arxiv.org/abs/2209.04021
It is known that the identity component of the automorphism group of a projective algebraic variety is an algebraic group. This is not true in general for quasi-projective varieties. In this note we address the question: given an affine algebraic sur
Externí odkaz:
http://arxiv.org/abs/2208.09738
Autor:
Perepechko, Alexander, Regeta, Andriy
Given an affine algebraic variety $X$, we prove that if the neutral component $\mathrm{Aut}^\circ(X)$ of the automorphism group consists of algebraic elements, then it is nested, i.e., is a direct limit of algebraic subgroups. This improves our earli
Externí odkaz:
http://arxiv.org/abs/2203.08950
Publikováno v:
In Bulletin des sciences mathématiques May 2024 192
Autor:
Perepechko, Alexander
Publikováno v:
Forum Mathematicum 33, no. 2 (2021), pp. 339-348
Let Y be a smooth del Pezzo surface of degree 3 polarized by a very ample divisor that is not proportional to the anticanonical one. Then the affine cone over Y is flexible in codimension one. Equivalently, such a cone has an open subset with an infi
Externí odkaz:
http://arxiv.org/abs/2006.16417
Publikováno v:
Mediterranean Journal of Mathematics, vol. 18, Article number: 267 (2021)
Rota-Baxter operators present a natural generalisation of integration by parts formula for the integral operator. In 2015, Zheng, Guo, and Rosenkranz conjectured that every injective Rota-Baxter operator of weight zero on the polynomial algebra $\mat
Externí odkaz:
http://arxiv.org/abs/2005.14030
Autor:
Perepechko, Alexander, Regeta, Andriy
Publikováno v:
Transformation Groups 28 (2023), pp. 401-412
For an affine algebraic variety $X$, we study the subgroup $\mathrm{Aut}_{\text{alg}}(X)$ of the group of regular automorphisms $\mathrm{Aut}(X)$ of $X$ generated by all the connected algebraic subgroups. We prove that $\mathrm{Aut}_{\text{alg}}(X)$
Externí odkaz:
http://arxiv.org/abs/1903.07699
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