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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
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
Citation:
Vik. S. Kulikov, V. M. Kharlamov, “On real structures on rigid surfaces”, Izv. Math., 66:1 (2002), 133–150
Linking options:
https://www.mathnet.ru/eng/im374https://doi.org/10.1070/IM2002v066n01ABEH000374 https://www.mathnet.ru/eng/im/v66/i1/p133
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Abstract page: | 658 | Russian version PDF: | 234 | English version PDF: | 30 | References: | 83 | First page: | 1 |
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