Generators for the tautological algebra of the moduli space of curves.
type: Item
instance of: scholarly article
title: Generators for the tautological algebra of the moduli space of curves.
zbMATH Open document ID: 1054.32008
DOI: 10.1016/S0040-9383(02)00082-4
author: Shigeyuki Morita
published in: Topology
publication date: 2003-04-27T00:00:00Z
review text: The author proves that the tautological algebra in cohomology of the moduli space \(M_g\) of smooth projective curves of genus \(g\) is generated by the first \([g/3]\) Mumford-Morita-Miller classes. This solves a part of \textit{C. Faber}'s conjecture [Moduli of curves and Abelian varieties. Aspects Math. E 33, 109--129 (1999; Zbl 0978.14029)] concerning the structure of the tautological algebra affirmatively. More precisely, for any \(k\) he writes the kth Mumford-Morita-Miller class \(e_k\) as an explicit polynomial in the lower classes for all genera \(g=3k-1,3k-2,\dots,2\).
Mathematics Subject Classification ID: 32G15
Mathematics Subject Classification ID: 57R20
Mathematics Subject Classification ID: 14H10
Mathematics Subject Classification ID: 57N05
Mathematics Subject Classification ID: 55R40
Mathematics Subject Classification ID: 57M99
zbMATH DE Number: 1900971
zbMATH Keywords: moduli space of curves
zbMATH Keywords: mapping class group
zbMATH Keywords: Mumford-Morita-Miller class
zbMATH Keywords: tautological algebra
zbMATH Keywords: symplectic group
reviewed by: Rubén A. Hidalgo
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1900971