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arXiv · 0805.2534

The rationality of certain moduli spaces of curves of genus 3

Ingrid Bauer·Fabrizio Catanese
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Abstract

We show, for each algebraically closed field, the rationality of the following two moduli spaces: M(3,3) parametrizing pairs (C, η) where C has genus 3 and ηis a 3-torsion divisor class, respectively of M(3,<3>) parametrizing pairs (C, <η>) as above and where <η> is the cyclic subgroup of order 3 in Pic_0(C) generated by η.

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Ingrid Bauer, Fabrizio Catanese. 2008-05-16. The rationality of certain moduli spaces of curves of genus 3. https://arxiv.org/abs/0805.2534

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