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 $K^{2}=8$.References
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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