Virasoro constraints and the Chern classes of the Hodge bundle

Abstract

We analyse the consequences of the Virasoro conjecture of Eguchi, Hori and Xiong for Gromov-Witten invariants, in the case of zero degree maps to the manifolds CP^1 and CP^2 (or more generally, smooth projective curves and smooth simply-connected projective surfaces). We obtain predictions involving intersections of psi and lambda classes on the compactification of M_{g,n}. In particular, we show that the Virasoro conjecture for CP^2 implies the numerical part of Faber's conjecture on the tautological Chow ring of M_g.

12 pages, latex2e

References in corpus (3)

• Quantum Cohomology and Virasoro Algebra
• A non-vanishing result for the tautological ring of {\cal M}_g
• A conjectural description of the tautological ring of the moduli space of curves

Cited by in corpus (63)

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• The Toda conjecture
• New results of intersection numbers on moduli spaces of curves
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• Algebraic structures on the topology of moduli spaces of curves and maps
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• A proof of the Faber intersection number conjecture
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• Complete descriptions of the tautological rings of the moduli spaces of curves of genus lower or equal to 4 with marked points
• A combinatorial proof of the ${\lambda }_g$ conjecture in genus 2
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