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

 

On the classification of irregular surfaces
of general type with
nonbirational bicanonical map


Authors: Fabrizio Catanese, Ciro Ciliberto and Margarida Mendes Lopes
Journal: Trans. Amer. Math. Soc. 350 (1998), 275-308
MSC (1991): Primary 14J29
MathSciNet review: 1422597
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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
Email: catanese@uni-math.gwdg.de

Ciro Ciliberto
Affiliation: Dipartimento di Matematica, Università di Tor Vergata, Viale della Ric. Scientifica, 16132 Roma, Italy
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

DOI: http://dx.doi.org/10.1090/S0002-9947-98-01948-5
PII: S 0002-9947(98)01948-5
Received by editor(s): February 22, 1996
Article copyright: © Copyright 1998 American Mathematical Society