Motivated by several recent results on the geometry of the moduli spaces $\overline{\Cal M}_{g,n}$ of stable curves of genus $g$ with $n$ marked points, we determine here 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 $1\le n\le 12$.
On the rationality of moduli spaces of pointed curves / Casnati, Gianfranco; Fontanari, Claudio. - In: JOURNAL OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6107. - 75:(2007), pp. 582-596.
On the rationality of moduli spaces of pointed curves
CASNATI, GIANFRANCO;FONTANARI, CLAUDIO
2007
Abstract
Motivated by several recent results on the geometry of the moduli spaces $\overline{\Cal M}_{g,n}$ of stable curves of genus $g$ with $n$ marked points, we determine here 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 $1\le n\le 12$.Pubblicazioni consigliate
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https://hdl.handle.net/11583/1640651
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