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Letbe the (coarse) moduli space of smooth curves of genus 7 with  n ≥0 marked points defined over the complex field. We denote bythe locus of points insiderepresenting curves carrying a. It is classically known thatis irreducible of dimension 17+ n . We prove in this paper thatis rational for 0≤ n ≤11.

Birational Properties of Some Moduli Spaces Related to Tetragonal Curves of Genus 7