Equivariant cohomology of moduli spaces of genus three curves with level two structure. (English) Zbl 1423.14182
The author studies the cohomology of various moduli spaces of curves of genus \(3\) with level \(2\) structures, including the moduli space \(\mathcal M_3[2]\) of genus \(3\) curves with level \(2\) structure, the moduli space \(\mathcal M_{3,1}[2]\) of genus \(3\) curves with level \(2\) structure and one marked point, and the moduli space \(\mathcal{H}ol_3[2]\) of genus \(3\) curves with level \(2\) structure with a holomorphic differential (or canonical divisor). The core of the study is to compute the cohomology of the moduli space \(\mathcal Q[2]\) of plane quartics with level \(2\) structure as a representation of \(\mathrm{Sp}(6, \mathbb F_2)\).
Reviewer: Dawei Chen (Chestnut Hill)
MSC:
| 14H10 | Families, moduli of curves (algebraic) |
| 14F25 | Classical real and complex (co)homology in algebraic geometry |
| 14H50 | Plane and space curves |
| 14J10 | Families, moduli, classification: algebraic theory |
| 14N20 | Configurations and arrangements of linear subspaces |
Keywords:
moduli spaces; curves of low genus; plane quartics; Del Pezzo surfaces; configurations of point sets; equivariant cohomologyReferences:
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