In algebraic geometry, the Virasoro conjecture states that a certain generating function encoding GromovâÂÂWitten invariants of a smooth projective variety is fixed by an action of half of the Virasoro algebra. The Virasoro conjecture is named after theoretical physicist Miguel ÃÂngel Virasoro. proposed the Virasoro conjecture as a generalization of Witten's conjecture. gave a survey of the Virasoro conjecture.
The proof of the genus 0 Virasoro conjecture for all smooth projective varieties (or more generally, compact symplectic manifolds) was first given by Xiaobo Liu and Gang Tian (1998).