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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Additive actions on toric varieties
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by Ivan Arzhantsev and Elena Romaskevich PDF
Proc. Amer. Math. Soc. 145 (2017), 1865-1879 Request permission

Abstract:

By an additive action on an algebraic variety $X$ of dimension $n$ we mean a regular action $\mathbb {G}_a^n\times X\to X$ with an open orbit of the commutative unipotent group $\mathbb {G}_a^n$. We prove that if a complete toric variety $X$ admits an additive action, then it admits an additive action normalized by the acting torus. Normalized additive actions on a toric variety $X$ are in bijection with complete collections of Demazure roots of the fan $\Sigma _X$. Moreover, any two normalized additive actions on $X$ are isomorphic.
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Additional Information
  • Ivan Arzhantsev
  • Affiliation: Faculty of Computer Science, National Research University Higher School of Economics, Kochnovskiy Proezd 3, Moscow, 125319 Russia
  • MR Author ID: 359575
  • Email: arjantsev@hse.ru
  • Elena Romaskevich
  • Affiliation: Yandex, ulica L’va Tolstogo 16, Moscow, 119034 Russia
  • MR Author ID: 1047535
  • Email: lena.apq@gmail.com
  • Received by editor(s): October 30, 2015
  • Received by editor(s) in revised form: June 26, 2016
  • Published electronically: October 26, 2016
  • Additional Notes: The research of the first author was supported by the grant RSF-DFG 16-41-01013.
  • Communicated by: Lev Borisov
  • © Copyright 2016 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 145 (2017), 1865-1879
  • MSC (2010): Primary 14L30, 14M25; Secondary 13N15, 14J50, 14M17
  • DOI: https://doi.org/10.1090/proc/13349
  • MathSciNet review: 3611303