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한국고등과학원 세미나 



A characterization of Inoue surfaces with p_g=0 and K^2=7 

Inoue constructed the first examples of smooth minimal complex surfaces of general type with $p_g=0$ and $K^2=7$. These surfaces are finite Galois covers of the $4$nodal cubic surface with the Galois group, the Klein group $mathbb{Z}_2times mathbb{Z}_2$. 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 selfintersection number $0$ and the other is a genus $2$ curve with selfintersection number $1$. In this talk, we conversely assume that $S$ is a smooth minimal complex surface of general type with $p_g=0$, $K^2=7$ and having an involution $sigma$. And we show that, if the divisorial part of the fixed locus of $sigma$ consists of two irreducible components $R_1$ and $R_2$, with $g(R_1)=3, R_1^2=0, g(R_2)=2$ and $R_2^2=1$, then the Klein group $mathbb{Z}_2times mathbb{Z}_2$ acts faithfully on $S$ and $S$ is indeed an Inoue surface. This is a joint work with Yifan Chen. 







