Relative virtual localization and vanishing of tautological classes on moduli spaces of curves
Authors:
Top Cited Papers
- 1 October 2005
- journal article
- Published by Duke University Press in Duke Mathematical Journal
- Vol. 130 (1) , 1-37
Abstract
We prove a localization formula for the moduli space of stable relative maps. As an application, we prove that all codimension i tautological classes on the moduli space of stable pointed curves vanish away from strata corresponding to curves with at least i-g+1 genus 0 components. As consequences, we prove and generalize various conjectures and theorems about various moduli spaces of curves (due to Diaz, Faber, Getzler, Ionel, Looijenga, Pandharipande, and others). This theorem appears to be the geometric content behind these results; the rest is straightforward graph combinatorics. The theorem also suggests the importance of the stratification of the moduli space by the number of rational components.Keywords
All Related Versions
This publication has 36 references indexed in Scilit:
- Hurwitz numbers and intersections on moduli spaces of curvesInventiones Mathematicae, 2001
- On Hurwitz numbers and Hodge integralsComptes Rendus de l'Académie des Sciences - Series I - Mathematics, 1999
- A Conjectural Description of the Tautological Ring of the Moduli Space of Curves1999
- Counting plane curves of any genusInventiones Mathematicae, 1998
- The intrinsic normal coneInventiones Mathematicae, 1997
- On the projectivity of the moduli spaces of curves.Journal für die reine und angewandte Mathematik (Crelles Journal), 1993
- Chow Rings of Moduli Spaces of Curves I: The Chow Ring of $\overbar{\mathcal{M}}_3$Annals of Mathematics, 1990
- Chow Rings of Moduli Spaces of Curves II: Some Results on the Chow Ring of ℳ 4Annals of Mathematics, 1990
- Complete subvarieties of the moduli space of smooth curves1987
- The Picard groups of the moduli spaces of curvesTopology, 1987