Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 
 

 

Flexibility of normal affine horospherical varieties


Authors: Sergey Gaifullin and Anton Shafarevich
Journal: Proc. Amer. Math. Soc. 147 (2019), 3317-3330
MSC (2010): Primary 13N15, 14J50; Secondary 14R20, 13A50
DOI: https://doi.org/10.1090/proc/14528
Published electronically: April 8, 2019
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We investigate flexibility of affine varieties with an action of a linear algebraic group. Flexibility of a smooth affine variety with only constant invertible functions and a locally transitive action of a reductive group is proved. Also we show that a normal affine complexity-zero horospherical variety with only constant invertible functions is flexible.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 13N15, 14J50, 14R20, 13A50

Retrieve articles in all journals with MSC (2010): 13N15, 14J50, 14R20, 13A50


Additional Information

Sergey Gaifullin
Affiliation: Faculty of Mechanics and Mathematics, Department of Higher Algebra, Lomonosov Moscow State University, Leninskie Gory 1, Moscow, 119991 Russia; Faculty of Computer Science, National Research University Higher School of Economics, Kochnovskiy Proezd 3, Moscow, 125319 Russia
Email: sgayf@yandex.ru

Anton Shafarevich
Affiliation: Faculty of Mechanics and Mathematics, Department of Higher Algebra, Lomonosov Moscow State University, Leninskie Gory 1, Moscow, 119991 Russia; Faculty of Computer Science, National Research University Higher School of Economics, Kochnovskiy Proezd 3, Moscow, 125319 Russia
Email: shafarevich.a@gmail.com

DOI: https://doi.org/10.1090/proc/14528
Keywords: Affine variety, automorphism, flexible variety, horospherical variety, locally nilpotent derivation, linear group action
Received by editor(s): May 16, 2018
Received by editor(s) in revised form: November 30, 2018
Published electronically: April 8, 2019
Additional Notes: The first author was supported by the Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS”
Communicated by: Jerzy Weyman
Article copyright: © Copyright 2019 American Mathematical Society