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On the rationality of moduli spaces of pointed curves
Author(s) -
Casnati Gianfranco,
Fontanari Claudio
Publication year - 2007
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdm011
Subject(s) - rationality , moduli , moduli space , pure mathematics , mathematics , moduli of algebraic curves , mathematical economics , philosophy , physics , epistemology , quantum mechanics
Motivated by several recent results on the geometry of the moduli spacesM¯ g , nof 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, ℳ g,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