Cohomology of the moduli space of curves of genus three with level two structure

Author: Olof Bergvall; Carel Faber; Jonas Bergström; Johannes Nicaise; Stockholms Universitet; []

Keywords: NATURAL SCIENCES; NATURVETENSKAP; NATURVETENSKAP; NATURAL SCIENCES; Algebraic geometry; Moduli space; Cohomology; Symplectic structure; Point count; matematik; Mathematics;

Abstract: In this thesis we investigate the moduli space M3[2] of curves of genus 3 equipped with a symplectic level 2 structure. In particular, we are interested in the cohomology of this space. We obtain cohomological information by decomposing M3[2] into a disjoint union of two natural subspaces, Q[2] and H3[2], and then making S7- resp. S8-equivariantpoint counts of each of these spaces separately.

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