Rationality and Chow-Kuenneth decompositions for some moduli stacks of curves

Details Rationality and Chow-Kuenneth decompositions for some moduli stacks of curves Rationality and Chow-Kuenneth decompositions for some moduli stacks of curves

2009-06-03

arxiv.org/abs/0906.0683v2

Mathematics

Algebraic Geometry

Some errors are corrected and new remarks are included

Scientific paper

In this paper, we show the existence of a Chow--Kuenneth decomposition for the moduli stack of stable curves of genus g with r marked points, for low values of g,r. We also look at the moduli space R of double covers of genus 3 curves, branched along 4 distinct points. We obtain a birational model of the moduli space R as a group quotient of a product of two Grassmanian varieties. This provides a Chow-Kuenneth decomposition over an open subset of R. The question of rationality of R is also discussed.

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