On the Kodaira dimension of the moduli space of curves. II: The even-genus case
type: Item
instance of: scholarly article
title: On the Kodaira dimension of the moduli space of curves. II: The even-genus case
zbMATH Open document ID: 0542.14014
DOI: 10.1007/BF01388638
published in: Inventiones Mathematicae
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143105
review text: This is a continuation of the author's joint paper with \textit{D. Mumford} [Invent. Math. 67, 23-86 (1982; Zbl 0506.14016)]. Here the author proves the following very important theorem: for g even and \(\geq 40\) the moduli space \(M_ g\) of curves of genus g is of general type. The main point is the hard calculation of a few intersection numbers, hence the proof of a few enumerative formulas about \(g^ 1_ d\) on a general curve. Recently \textit{D. Eisenbud} and the author [Bull. Am. Math. Soc. 10, 277-280 (1984; Zbl 0533.14013)] announced that \(M_ g\) is of general type if \(g\geq 24\).
Mathematics Subject Classification ID: 14H10
Mathematics Subject Classification ID: 14C20
Mathematics Subject Classification ID: 14D20
Mathematics Subject Classification ID: 14H30
zbMATH DE Number: 3861319
zbMATH Keywords: canonical divisor
zbMATH Keywords: Hurwitz scheme
zbMATH Keywords: Chern classes
zbMATH Keywords: Kodaira dimension
zbMATH Keywords: moduli space of curves of general type
author: Joe Harris
MaRDI profile type: Publication
cites work: Q3347989
cites work: Q4342000
cites work: Q4195061
cites work: The second homology group of the mapping class group of an orientable surface
cites work: On the Kodaira dimension of the moduli space of curves
cites work: Stability of projective varieties
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description: scientific article; zbMATH DE number 3861319