Virasoro constraints and the Chern classes of the Hodge bundle

Details Virasoro constraints and the Chern classes of the Hodge bundle Virasoro constraints and the Chern classes of the Hodge bundle

1998-05-25

arxiv.org/abs/math/9805114v1

Mathematics

Algebraic Geometry

12 pages, latex2e

Scientific paper

10.1016/S0550-3213(98)00517-3

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.

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