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arXiv · 1105.0310

Birational properties of some moduli spaces related to tetragonal curves of genus 7

Christian Böhning·Hans-Christian Graf von Bothmer·Gianfranco Casnati
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Abstract

Let M_{7,n} be the (coarse) moduli space of smooth curves of genus 7 with n marked points defined over the complex field. We denote by M^1_{7,n;4} the locus of points inside M_{7,n} representing curves carrying a g^1_4. It is classically known that M^1_{7,n;4} is irreducible of dimension 17+n. We prove in this paper that M^1_{7,n;4} is rational for 0<= n <= 11.

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Christian Böhning, Hans-Christian Graf von Bothmer, Gianfranco Casnati. 2011-07-06. Birational properties of some moduli spaces related to tetragonal curves of genus 7. https://doi.org/10.1093/imrn%2Frnr230

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