On the rationality of moduli spaces of pointed curves

Details On the rationality of moduli spaces of pointed curves On the rationality of moduli spaces of pointed curves

2005-04-12

arxiv.org/abs/math/0504249v3

Mathematics

Algebraic Geometry

Final version accepted for publication on the Journal of the London Mathematical Society (Section 6 of the previous version ha

Scientific paper

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 $1\le n\le 12$.

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