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Journal of the London Mathematical Society Advance Access originally published online on June 20, 2007
Journal of the London Mathematical Society 2007 75(3):582-596; doi:10.1112/jlms/jdm011
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© 2007 London Mathematical Society

On the rationality of moduli spaces of pointed curves

Gianfranco Casnati and Claudio Fontanari

Dipartimento di Matematica
Politecnico di Torino
c.so Duca degli Abruzzi 24
10129 Torino
Italy
claudio.fontanari{at}polito.it

Motivated by several recent results on the geometry of the moduli spaces Formula of stable curves of genus g with n marked points, we determine the birational structure of these spaces for small values of g and n by exploiting suitable plane models of a general curve. More precisely, Mg,n is shown to be rational for g = 2 and 1 <= n <= 12, g = 3 and 1 <= n <= 14, g = 4 and 1 <= n <= 15, and g = 5 and 1 <= n <= 12

casnati{at}calvino.polito.it

2000 Mathematics Subject Classification 14H10, 14H45, 14E08, 14L30.

Received June 15, 2005; revised November 21, 2006; published online June 20, 2007.


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