@article{ce76a76b928246629b852f854526f94a,
title = "Flexible affine cones and flexible coverings",
abstract = "We provide a new criterion for flexibility of affine cones over varieties covered by flexible affine varieties. We apply this criterion to prove flexibility of affine cones over secant varieties of Segre–Veronese embeddings and over certain Fano threefolds. We further prove flexibility of total coordinate spaces of Cox rings of del Pezzo surfaces.",
keywords = "Affine cone, Automorphism group, Cox ring, Del Pezzo surface, Flexibility, Secant variety, Segre–Veronese embedding, Transitivity",
author = "Mateusz Michalek and Alexander Perepechko and Hendrik S{\"u}{\ss}",
note = "Funding Information: The research of M. Michalek was supported by IP Grant 0301/IP3/2015/73 of the Polish Ministry of Science. Funding Information: Acknowledgements Open access funding provided by Max Planck Society. We would like to thank Mikhail Zaidenberg for motivating questions and inspiring results and Ivan Arzhantsev for many useful remarks and suggestions. The first author started the project under Mobilnosc+ Polish Ministry of Science program, finished under DAAD PRIME program and was supported by the Foundation for Polish Science (FNP). The formulation and proof of Lemma 1.1 (A.Perepechko) were supported by a Grant from the Dynasty Foundation. The research of A. Perepechko, which lead to the results of Sect. 5, was carried out at the IITP RAS at the expense of the Russian Foundation for Sciences (Project no. 14-50-00150). Publisher Copyright: {\textcopyright} 2018, The Author(s). Copyright: Copyright 2018 Elsevier B.V., All rights reserved.",
year = "2018",
month = jun,
day = "5",
doi = "10.1007/s00209-018-2069-2",
language = "English",
volume = "290",
pages = "1457--1478",
journal = "Mathematische Zeitschrift",
issn = "0025-5874",
publisher = "Springer New York",
number = "3-4",
}