Let $S$ be a minimal complex surface of general type and of maximal Albanese dimension; by the Severi inequality one has $K^2_S\ge 4\chi(\mathcal O_S)$. We prove that the equality $K^2_S=4\chi(\mathcal O_S)$ holds if and only if $q(S):= h^1(\mathcal O_S)=2$ and the canonical model of $S$ is a double cover of the Albanese surface branched on an ample divisor with at most negligible singularities.
Surfaces on the Severi line
STOPPINO, LIDIA
2016-01-01
Abstract
Let $S$ be a minimal complex surface of general type and of maximal Albanese dimension; by the Severi inequality one has $K^2_S\ge 4\chi(\mathcal O_S)$. We prove that the equality $K^2_S=4\chi(\mathcal O_S)$ holds if and only if $q(S):= h^1(\mathcal O_S)=2$ and the canonical model of $S$ is a double cover of the Albanese surface branched on an ample divisor with at most negligible singularities.
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