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Quotients of del Pezzo surfaces of high degree


Author: Andrey Trepalin
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 14E08, 14M20; Secondary 14E07
DOI: https://doi.org/10.1090/tran/7130
Published electronically: December 27, 2017
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Abstract: In this paper we study quotients of del Pezzo surfaces of degree four and more over arbitrary field $ \Bbbk $ of characteristic zero by finite groups of automorphisms. We show that if a del Pezzo surface $ X$ contains a point defined over the ground field and the degree of $ X$ is at least five, then the quotient is always $ \Bbbk $-rational. If the degree of $ X$ is equal to four, then the quotient can be non-$ \Bbbk $-rational only if the order of the group is $ 1$, $ 2$, or $ 4$. For these groups we construct examples of non-$ \Bbbk $-rational quotients.


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Additional Information

Andrey Trepalin
Affiliation: Institute for Information Transmission Problems, 19 Bolshoy Karetnyi side-street, Moscow 127994, Russia — and — Laboratory of Algebraic Geometry, National Research University Higher School of Economics, 6 Usacheva street, Moscow 119048, Russia
Email: trepalin@mccme.ru

DOI: https://doi.org/10.1090/tran/7130
Received by editor(s): June 2, 2015
Received by editor(s) in revised form: October 12, 2016
Published electronically: December 27, 2017
Additional Notes: The author was supported by the Russian Academic Excellence Project ‘5–100’, Young Russian Mathematics award, and the grant RFFI 15-01-02164-a
Article copyright: © Copyright 2017 American Mathematical Society

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