Rationality and Chow-Kuenneth decompositions for some moduli stacks of curves
Algebraic Geometry
2014-10-28 v2 Commutative Algebra
Abstract
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.
Cite
@article{arxiv.0906.0683,
title = {Rationality and Chow-Kuenneth decompositions for some moduli stacks of curves},
author = {JN Iyer and S. Müller-Stach},
journal= {arXiv preprint arXiv:0906.0683},
year = {2014}
}
Comments
Some errors are corrected and new remarks are included