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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2022, Volume 318, Pages 43–50
DOI: https://doi.org/10.4213/tm4292 (Mi tm4292) 		 
Orbits of the Automorphism Group of Horospherical Varieties, and Divisor Class Group

Sergey A. Gaifullinab

a Faculty of Computer Science, HSE University, Pokrovskii bul. 11, Moscow, 109028 Russia
b Moscow Center of Fundamental and Applied Mathematics, Moscow, 119991 Russia
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DOI: https://doi.org/10.4213/tm4292
Abstract: In 2013 Bazhov proved a criterion for two points on a complete toric variety to lie in the same orbit of the neutral component of the automorphism group. This criterion is formulated in terms of the divisor class group. The same year Arzhantsev and Bazhov obtained a similar criterion for affine toric varieties. We prove a necessary condition similar to this criterion in the cases of affine and projective horospherical varieties.
Keywords: horospherical variety, toric variety, divisor class group, automorphism, locally nilpotent derivation.
Funding agency Grant number
Russian Science Foundation 20-71-00109
This work is supported by the Russian Science Foundation under grant no. 20-71-00109, https://rscf.ru/project/20-71-00109/.
Received: May 11, 2022
Revised: June 13, 2022
Accepted: June 16, 2022
English version:
Proceedings of the Steklov Institute of Mathematics, 2022, Volume 318, Pages 38–44
DOI: https://doi.org/10.1134/S0081543822040046
Bibliographic databases:
Document Type: Article
UDC: 512.745
MSC: Primary 14R20, 14J50; Secondary 13A50, 14M25
Language: Russian
Citation: Sergey A. Gaifullin, “Orbits of the Automorphism Group of Horospherical Varieties, and Divisor Class Group”, Toric Topology, Group Actions, Geometry, and Combinatorics. Part 2, Collected papers, Trudy Mat. Inst. Steklova, 318, Steklov Math. Inst., Moscow, 2022, 43–50; Proc. Steklov Inst. Math., 318 (2022), 38–44
Citation in format AMSBIB
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\by Sergey~A.~Gaifullin
\paper Orbits of the Automorphism Group of Horospherical Varieties, and Divisor Class Group
\inbook Toric Topology, Group Actions, Geometry, and Combinatorics. Part~2
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
\yr 2022
\vol 318
\pages 43--50
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4292}
\crossref{https://doi.org/10.4213/tm4292}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4538834}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2022
\vol 318
\pages 38--44
\crossref{https://doi.org/10.1134/S0081543822040046}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85142067311}
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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