On the rationality of moduli spaces of pointed curves
Loading...
Date
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
Motivated by several recent results on the geometry of the moduli spaces $\bar{\Cal M}_{g,n}$ of stable curves of genus $g$ with $n$ marked points, here we determine their birational structure for small values of $g$ and $n$ by exploiting suitable plane models of the general curve. More precisely, we show that ${\Cal M}_{g,n}$ is rational for $g=2$ and $1\le n\le 12$, $g=3$ and $1\le n\le 14$, $g=4$ and $1\le n\le 15$, $g=5$ and $1\le n\le 12$.
Final version accepted for publication on the Journal of the London Mathematical Society (Section 6 of the previous version has been removed since the proof of Claim 6.3 contained a gap)
Final version accepted for publication on the Journal of the London Mathematical Society (Section 6 of the previous version has been removed since the proof of Claim 6.3 contained a gap)