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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2022, Volume 503, Pages 5–10
DOI: https://doi.org/10.31857/S2686954322020059 (Mi danma239) 		 
This article is cited in 1 scientific paper (total in 1 paper)

MATHEMATICS

On the existence of $B$-root subgroups on affine spherical varieties

R. S. Avdeeva, V. S. Zhgoonb

a National Research University "Higher School of Economics", Moscow
b Scientific Research Institute for System Studies of RAS, Moscow
Citations (1)
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DOI: https://doi.org/10.31857/S2686954322020059
Abstract: Let $X$ be an irreducible affine algebraic variety that is spherical with respect to an action of a connected reductive group $G$. In this paper, we provide sufficient conditions, formulated in terms of weight combinatorics, for the existence of one-parameter additive actions on $X$ normalized by a Borel subgroup $B\subset G$. As an application, we prove that every $G$-stable prime divisor in $X$ can be connected with an open $G$-orbit by means of a suitable $B$-normalized one-parameter additive action.
Keywords: additive group action, toric variety, spherical variety, Demazure root, locally nilpotent derivation, local structure theorem.
Funding agency Grant number
Russian Science Foundation 22-41-02019
Ministry of Education and Science of the Russian Federation FNEF-2022-0011
HSE Basic Research Program
The research of R.S. Avdeev was supported by the Russian Science Foundation, grant no. 22-41-02019. The research of V.S. Zhgoon was performed within the state assignment for basic scientific research (project no. FNEF-2022-0011) and the HSE University Basic Research Program.
Presented: V. P. Platonov
Received: 22.12.2021
Revised: 22.12.2021
Accepted: 28.12.2021
English version:
Doklady Mathematics, 2022, Volume 105, Issue 2, Pages 51–55
DOI: https://doi.org/10.1134/S1064562422020053
Bibliographic databases:
Document Type: Article
UDC: 512.745.2
Language: Russian
Citation: R. S. Avdeev, V. S. Zhgoon, “On the existence of $B$-root subgroups on affine spherical varieties”, Dokl. RAN. Math. Inf. Proc. Upr., 503 (2022), 5–10; Dokl. Math., 105:2 (2022), 51–55
Citation in format AMSBIB
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\by R.~S.~Avdeev, V.~S.~Zhgoon
\paper On the existence of $B$-root subgroups on affine spherical varieties
\jour Dokl. RAN. Math. Inf. Proc. Upr.
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\vol 503
\pages 5--10
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\crossref{https://doi.org/10.31857/S2686954322020059}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4448465}
\elib{https://elibrary.ru/item.asp?id=48506193}
\transl
\jour Dokl. Math.
\yr 2022
\vol 105
\issue 2
\pages 51--55
\crossref{https://doi.org/10.1134/S1064562422020053}
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