Virasoro constraints and the Chern classes of the Hodge bundle Original Research Article

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 P1and P2 (or more generally, smooth projective curves and smooth simply connected projective surfaces). We obtain predictions involving intersections of psi and lambda classes on Mg,n. In particular, we show that the Virasoro conjecture for P2 implies the numerical part of Faberʹs conjecture on the tautological Chow ring of Mg.