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Rational cohomology of the moduli space of genus 4 curves

Published online by Cambridge University Press:  10 February 2005

Orsola Tommasi
Orsola Tommasi
Affiliation:
Department of Mathematics, University of Nijmegen, Toernooiveld, 6525 ED Nijmegen, The Netherlandstommasi@math.kun.nl
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Abstract

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We compute the mixed Hodge structure on the rational cohomology of the moduli space of smooth genus 4 curves. Specifically, we prove that its Poincaré–Serre polynomial is 1 + t2u2 + t4u4 + t5u6. We show this by producing a stratification of the space, such that all strata are geometric quotients of complements of discriminants.

Keywords

rational cohomologymoduli of curvesdiscriminants14H10 (primary)55R8014R3014F99 (secondary)
Type
Research Article
Information
Compositio Mathematica , Volume 141 , Issue 2 , March 2005 , pp. 359 - 384
Copyright
Foundation Compositio Mathematica 2005