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 ℙ1 and ℙ2 (or more generally, smooth projective curves and smooth simply connected protective surfaces). We obtain predictions involving intersections of psi and lambda classes on M̄g,n. In particular, we show that the Virasoro conjecture for ℙ2 implies the numerical part of Faber's conjecture on the tautological Chow ring of Mg.
- Gromov-Witten invariants
- Topological gravity
- Virasoro conjecture
ASJC Scopus subject areas
- Nuclear and High Energy Physics