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摘要
Inoue constructed the first examples of smooth minimal complex surfaces of general type with pg = 0 and K2 = 7. These surfaces are finite Galois covers of the 4- nodal cubic surface with the Galois group, the Klein group Z(2) x Z(2). For such a surface S, the bicanonical map of S has degree 2 and it is composed with exactly one involution in the Galois group. The divisorial part of the fixed locus of this involution consists of two irreducible components: one is a genus 3 curve with self- intersection number 0 and the other is a genus 2 curve with self- intersection number - 1. Conversely, assume that S is a smooth minimal complex surface of general type with pg = 0, K2 = 7 and having an involution s. We show that, if the divisorial part of the fixed locus of s consists of two irreducible components R1 and R2, with g(R1) = 3, R2 1 = 0, g(R2) = 2 and R2 2 = - 1, then the Klein group Z(2) x Z(2) acts faithfully on S and S is indeed an Inoue surface.
- 出版日期2018-12
- 单位北京航空航天大学
