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Cohomological and Geometric Approaches to Rationality Problems pp 1–16Cite as

The Rationality of Certain Moduli Spaces of Curves of Genus 3

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Part of the book series: Progress in Mathematics ((PM,volume 282))

Summary

We prove rationality of the moduli space of pairs of curves of genus three together with a point of order three in their Jacobian.

2000 Mathematics Subject Classification codes: 14E08, 14H10, 14H45

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References

  1. Bauer, I. and Catanese, F., Symmetry and variation of Hodge structures, Asian J. Math., vol.8, no.2, 363–390, (2004).

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  2. Bogomolov, F. A. and Katsylo, P. I., Rationality of some quotient varieties, Mat. Sb. (N.S.), vol. 126 (168), no. 4, 584–589, (1985).

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  3. Catanese, F., On the rationality of certain moduli spaces related to curves of genus 4, Algebraic geometry (Ann Arbor, Mich., 1981), 30–50, Lecture Notes in Math., 1008, Springer, Berlin (1983).

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Acknowledgments

The research of the authors was performed in the realm of the DFG Forschergruppe 790 “Classification of algebraic surfaces and compact complex manifolds.”

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Authors and Affiliations

  1. Mathematisches Institut Universität Bayreuth, II D-95440, Bayreuth, NW, Germany

    Ingrid Bauer & Fabrizio Catanese

Authors
  1. Ingrid Bauer
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  2. Fabrizio Catanese
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Corresponding author

Correspondence to Ingrid Bauer .

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Editors and Affiliations

  1. Department of Mathematics, Courant Institute of Math. Sciences, New York University, Mercer St. 251, New York, 10012, USA

    Fedor Bogomolov

  2. Department of Mathematics, Courant Institute of Math. Sciences, New York University, Mercer St. 251, New York, 10012, New York, USA

    Yuri Tschinkel

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Bauer, I., Catanese, F. (2010). The Rationality of Certain Moduli Spaces of Curves of Genus 3. In: Bogomolov, F., Tschinkel, Y. (eds) Cohomological and Geometric Approaches to Rationality Problems. Progress in Mathematics, vol 282. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4934-0_1

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