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Izvestiya: Mathematics, 2002, Volume 66, Issue 1, Pages 133–150
DOI: https://doi.org/10.1070/IM2002v066n01ABEH000374
(Mi im374)
 

This article is cited in 40 scientific papers (total in 40 papers)

On real structures on rigid surfaces

Vik. S. Kulikova, V. M. Kharlamovb

a Steklov Mathematical Institute, Russian Academy of Sciences
b University Louis Pasteur
References:
Abstract: We construct examples of rigid surfaces (that is, surfaces whose deformation class consists of a unique surface) with a particular behaviour with respect to real structures. In one example the surface has no real structure. In another it has a unique real structure, which is not maximal with respect to the Smith–Thom inequality. These examples give negative answers to the following problems: the existence of real surfaces in each deformation class of complex surfaces, and the existence of maximal real surfaces in every complex deformation class that contains real surfaces. Moreover, we prove that there are no real surfaces among surfaces of general type with $p_g=q=0$ and $K^2=9$.
These surfaces also provide new counterexamples to the “Dif = Def” problem.
Received: 09.01.2001
Bibliographic databases:
Document Type: Article
UDC: 512.7+515.1
MSC: 14P25, 14J29
Language: English
Original paper language: Russian
Citation: Vik. S. Kulikov, V. M. Kharlamov, “On real structures on rigid surfaces”, Izv. Math., 66:1 (2002), 133–150
Citation in format AMSBIB
\Bibitem{KulKha02}
\by Vik.~S.~Kulikov, V.~M.~Kharlamov
\paper On real structures on rigid surfaces
\jour Izv. Math.
\yr 2002
\vol 66
\issue 1
\pages 133--150
\mathnet{http://mi.mathnet.ru//eng/im374}
\crossref{https://doi.org/10.1070/IM2002v066n01ABEH000374}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1917540}
\zmath{https://zbmath.org/?q=an:1055.14060}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0042343154}
Linking options:
  • https://www.mathnet.ru/eng/im374
  • https://doi.org/10.1070/IM2002v066n01ABEH000374
  • https://www.mathnet.ru/eng/im/v66/i1/p133
  • This publication is cited in the following 40 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
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    Abstract page:658
    Russian version PDF:234
    English version PDF:30
    References:83
    First page:1
     
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