Izvestiya: Mathematics
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find






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


Izvestiya: Mathematics, 2004, Volume 68, Issue 5, Pages 965–1008
DOI: https://doi.org/10.1070/IM2004v068n05ABEH000505
(Mi im505)
 

This article is cited in 16 scientific papers (total in 16 papers)

Old and new examples of surfaces of general type with $p_g=0$

Vik. S. Kulikov

Steklov Mathematical Institute, Russian Academy of Sciences
References:
Abstract: We investigate surfaces of general type with geometric genus $p_g=0$ which may be given as Galois coverings of the projective plane branched over an arrangement of lines with Galois group $G=(\mathbb Z/q\mathbb Z)^k$, where $k\geqslant 2$ and $q$ is a prime. Examples of such coverings include the classical Godeaux surface, Campedelli surfaces, Burniat surfaces, and a new surface $X$ with invariants $K_X^2=6$ and $(\mathbb Z/3\mathbb Z)^3\subset\operatorname{Tors}(X)$. We prove that the automorphism group of a generic surface of Campedelli type is isomorphic to $(\mathbb Z/2\mathbb Z)^3$. We describe the irreducible components of the moduli space containing the Burniat surfaces. We also show that the Burniat surface $S$ with $K_S^2=2$ has torsion group $\operatorname{Tors}(S)\simeq(\mathbb Z/2\mathbb Z)^3$ (and hence belongs to the family of Campedelli surfaces), that is, the corresponding statement in [9], [4], and [1, p. 237], about the torsion group of the Burniat surface $S$ with $K_S^2=2$ is not correct.
Received: 13.04.2004
Bibliographic databases:
Document Type: Article
UDC: 512.7
Language: English
Original paper language: Russian
Citation: Vik. S. Kulikov, “Old and new examples of surfaces of general type with $p_g=0$”, Izv. Math., 68:5 (2004), 965–1008
Citation in format AMSBIB
\Bibitem{Kul04}
\by Vik.~S.~Kulikov
\paper Old and new examples of surfaces of general type with $p_g=0$
\jour Izv. Math.
\yr 2004
\vol 68
\issue 5
\pages 965--1008
\mathnet{http://mi.mathnet.ru//eng/im505}
\crossref{https://doi.org/10.1070/IM2004v068n05ABEH000505}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2104852}
\zmath{https://zbmath.org/?q=an:1073.14055}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000226062400005}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746475845}
Linking options:
  • https://www.mathnet.ru/eng/im505
  • https://doi.org/10.1070/IM2004v068n05ABEH000505
  • https://www.mathnet.ru/eng/im/v68/i5/p123
  • This publication is cited in the following 16 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:611
    Russian version PDF:253
    English version PDF:27
    References:93
    First page:1
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024