Duke Mathematical Journal

Relative virtual localization and vanishing of tautological classes on moduli spaces of curves

Tom Graber and Ravi Vakil

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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.

Article information

Source
Duke Math. J. Volume 130, Number 1 (2005), 1-37.

Dates
First available in Project Euclid: 12 November 2005

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1131804018

Digital Object Identifier
doi:10.1215/S0012-7094-05-13011-3

Mathematical Reviews number (MathSciNet)
MR2176546

Subjects
Primary: 14H10: Families, moduli (algebraic) 14D22: Fine and coarse moduli spaces
Secondary: 14C15: (Equivariant) Chow groups and rings; motives 14F43: Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies)

Citation

Graber, Tom; Vakil, Ravi. Relative virtual localization and vanishing of tautological classes on moduli spaces of curves. Duke Math. J. 130 (2005), no. 1, 1--37. doi:10.1215/S0012-7094-05-13011-3. http://projecteuclid.org/euclid.dmj/1131804018.


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