Surfaces with \(K^{2}=8, p_{g}=4\) and canonical involution. (English) Zbl 1181.14040

Bauer, Ingrid C.; Pignatelli, Roberto

Osaka J. Math. 46, No. 3, 799-820 (2009).

This paper is devoted to the complete classification of regular surfaces with \(K^2=8\), \(p_g=4\) whose canonical map is composed with an involution. It is shown that the quotient surface is either rational or of general type and in this last case the canonical map has degree 4.
Six unirational families of such surfaces are obtained of which two form irreducible components of the moduli space of surfaces with \(K^2=8\), \(p_g=4\). It is also shown that these surfaces hit three different topological types.

Reviewer: Margarida Mendes Lopes (Lisboa)

MSC:

14J29	Surfaces of general type
14J10	Families, moduli, classification: algebraic theory
14J50	Automorphisms of surfaces and higher-dimensional varieties

Keywords:

surfaces of general type; non birational canonical map; involution; automorphism of order 2; moduli space of surfaces with \(p_g=4\)

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