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On the rationality of moduli spaces of pointed curves

Gianfranco Casnati·Claudio Fontanari
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Abstract

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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Gianfranco Casnati, Claudio Fontanari. 2007-01-17. On the rationality of moduli spaces of pointed curves. https://arxiv.org/abs/math/0504249

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