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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Surfaces with $p_g=q=3$


Authors: Christopher D. Hacon and Rita Pardini
Journal: Trans. Amer. Math. Soc. 354 (2002), 2631-2638
MSC (2000): Primary 14J29
Published electronically: March 14, 2002
MathSciNet review: 1895196
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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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Additional Information

Christopher D. Hacon
Affiliation: Department of Mathematics, Surge Bldg., 2nd floor, University of California, Riverside, California 92521-0135
Email: hacon@math.ucr.edu

Rita Pardini
Affiliation: Dipartimento di Matematica, Università di Pisa, Via Buonarroti, 2, 56127 Pisa, Italy
Email: pardini@dm.unipi.it

DOI: http://dx.doi.org/10.1090/S0002-9947-02-02891-X
PII: S 0002-9947(02)02891-X
Received by editor(s): March 5, 2001
Published electronically: March 14, 2002
Article copyright: © Copyright 2002 American Mathematical Society