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

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

2011-05-02

arxiv.org/abs/1105.0310v2

Mathematics

Algebraic Geometry

20 pages; in the second version we replaced the previous Lemma 4.3 by Lemma 4.5, and fixed the proof of the rationality of the

Scientific paper

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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