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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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On the classification of irregular surfaces of general type with nonbirational bicanonical map
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by Fabrizio Catanese, Ciro Ciliberto and Margarida Mendes Lopes PDF
Trans. Amer. Math. Soc. 350 (1998), 275-308 Request permission

Abstract:

The present paper is devoted to the classification of irregular surfaces of general type with $p_{g}\geq 3$ and nonbirational bicanonical map. Our main result is that, if $S$ is such a surface and if $S$ is minimal with no pencil of curves of genus $2$, then $S$ is the symmetric product of a curve of genus $3$, and therefore $p_{g}=q=3$ and $K^{2}=6$. Furthermore we obtain some results towards the classification of minimal surfaces with $p_{g}=q=3$. Such surfaces have $6\leq K^{2}\leq 9$, and we show that $K^{2}=6$ if and only if $S$ is the symmetric product of a curve of genus $3$. We also classify the minimal surfaces with $p_{g}=q=3$ with a pencil of curves of genus $2$, proving in particular that for those one has $K^{2}=8$.
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Additional Information
  • Fabrizio Catanese
  • Affiliation: Dipartimento di Matematica, Università di Pisa, Via Buonarroti 2, 56127 Pisa, Italy
  • Address at time of publication: Mathematisches Institut der Georg-August, Universität Göttingen, Bunsenstraße 3-5, D-37073 Göttingen, Germany
  • MR Author ID: 46240
  • Email: catanese@uni-math.gwdg.de
  • Ciro Ciliberto
  • Affiliation: Dipartimento di Matematica, Università di Tor Vergata, Viale della Ric. Scientifica, 16132 Roma, Italy
  • MR Author ID: 49480
  • Email: cilibert@axp.mat.utovrm.it
  • Margarida Mendes Lopes
  • Affiliation: Dipartimento di Matemática, Faculdade de Ciencias de Lisboa, R. Ernesto de Vasconcelos, 1700 Lisboa, Portugal
  • Email: mmlopes@ptmat.lmc.fc.ul.pt
  • Received by editor(s): February 22, 1996
  • © Copyright 1998 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 350 (1998), 275-308
  • MSC (1991): Primary 14J29
  • DOI: https://doi.org/10.1090/S0002-9947-98-01948-5
  • MathSciNet review: 1422597