|
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
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
Citation:
Vik. S. Kulikov, “Old and new examples of surfaces of general type with $p_g=0$”, Izv. Math., 68:5 (2004), 965–1008
Linking options:
https://www.mathnet.ru/eng/im505https://doi.org/10.1070/IM2004v068n05ABEH000505 https://www.mathnet.ru/eng/im/v68/i5/p123
|
Statistics & downloads: |
Abstract page: | 611 | Russian version PDF: | 253 | English version PDF: | 27 | References: | 93 | First page: | 1 |
|