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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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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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Additional Information
  • Christopher D. Hacon
  • Affiliation: Department of Mathematics, Surge Bldg., 2nd floor, University of California, Riverside, California 92521-0135
  • MR Author ID: 613883
  • 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
  • Received by editor(s): March 5, 2001
  • Published electronically: March 14, 2002
  • © Copyright 2002 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 354 (2002), 2631-2638
  • MSC (2000): Primary 14J29
  • DOI: https://doi.org/10.1090/S0002-9947-02-02891-X
  • MathSciNet review: 1895196