Surfaces with 𝑝_{𝑔}=𝑞=3

Hacon, Christopher; Pardini, Rita

doi:10.1090/S0002-9947-02-02891-X

Surfaces with $p_g=q=3$
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by Christopher D. Hacon and Rita Pardini PDF

Trans. Amer. Math. Soc. 354 (2002), 2631-2638 Request permission

Abstract:

We classify minimal complex surfaces of general type with $p_g=q=3$. More precisely, we show that such a surface is either the symmetric product of a curve of genus $3$ or a free $\mathbb {Z}_2-$quotient of the product of a curve of genus $2$ and a curve of genus $3$. Our main tools are the generic vanishing theorems of Green and Lazarsfeld and the characterization of theta divisors given by Hacon in Corollary 3.4 of Fourier transforms, generic vanishing theorems and polarizations of abelian varieties.

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