Abstract
Let S be a minimal complex surface of general type and of maximal Albanese dimension; by the Severi inequality one has KS2≥4χ(OS). We prove that the equality KS2=4χ(OS) holds if and only if q(S):=h1(OS)=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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