Moscow Mathematical Journal
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mosc. Math. J.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mosc. Math. J., 2018, Volume 18, Number 3, Pages 557–597 (Mi mmj686)  

This article is cited in 1 scientific paper (total in 1 paper)

Quotients of del Pezzo surfaces of degree $2$

Andrey Trepalinab

a Institute for Information Transmission Problems, 19 Bolshoy Karetnyi side-str., Moscow 127994, Russia
b Laboratory of Algebraic Geometry, National Research University Higher School of Economics, 6 Usacheva str., Moscow 119048, Russia

Abstract: Let $\Bbbk$ be any field of characteristic zero, $X$ be a del Pezzo surface of degree $2$ and $G$ be a group acting on $X$. In this paper we study $\Bbbk$-rationality questions for the quotient surface $X / G$. If there are no smooth $\Bbbk$-points on $X / G$ then $X / G$ is obviously non-$\Bbbk$-rational. Assume that the set of smooth $\Bbbk$-points on the quotient is not empty. We find a list of groups such that the quotient surface can be non-$\Bbbk$-rational. For these groups we construct examples of both $\Bbbk$-rational and non-$\Bbbk$-rational quotients of both $\Bbbk$-rational and non-$\Bbbk$-rational del Pezzo surfaces of degree $2$ such that the $G$-invariant Picard number of $X$ is $1$. For all other groups we show that the quotient $X / G$ is always $\Bbbk$-rational.

Key words and phrases: Rationality problems, del Pezzo surfaces, Minimal model program, Cremona group.

DOI: https://doi.org/10.17323/1609-4514-2018-18-3-557-597

Full text: http://www.mathjournals.org/.../2018-018-003-007.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 14E08, 14M20, 14E07
Language:

Citation: Andrey Trepalin, “Quotients of del Pezzo surfaces of degree $2$”, Mosc. Math. J., 18:3 (2018), 557–597

Citation in format AMSBIB
\Bibitem{Tre18}
\by Andrey~Trepalin
\paper Quotients of del Pezzo surfaces of degree~$2$
\jour Mosc. Math.~J.
\yr 2018
\vol 18
\issue 3
\pages 557--597
\mathnet{http://mi.mathnet.ru/mmj686}
\crossref{https://doi.org/10.17323/1609-4514-2018-18-3-557-597}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000456105800007}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85053834923}


Linking options:
  • http://mi.mathnet.ru/eng/mmj686
  • http://mi.mathnet.ru/eng/mmj/v18/i3/p557

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. Trepalin, “Quotients of del Pezzo surfaces”, Int. J. Math., 30:12 (2019), 1950068  crossref  mathscinet  zmath  isi  scopus
  • Moscow Mathematical Journal
    Number of views:
    This page:87
    References:12

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021