%0 Journal Article
%T Birational properties of some moduli spaces related to tetragonal curves of genus 7
%A Christian B£¿hning
%A Hans-Christian Graf von Bothmer
%A Gianfranco Casnati
%J Mathematics
%D 2011
%I arXiv
%R 10.1093/imrn/rnr230
%X 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.
%U http://arxiv.org/abs/1105.0310v2