Eguchi–Hori–Xiong Virasoro constraints for the quantum cohomology partition function

Let $V$ be a Fano manifold with only even-dimensional cohomology classes, let $Z$ be the partition function of its topological sigma model coupled to gravity, and let $L_n$ for $n\in\mathbb{Z}$ be the linear differential operators on the big phase space constructed by Eguchi, Hori and Xiong. They satisfy the Virasoro commutation relations under the stated Chern-class condition.

Eguchi–Hori–Xiong conjecture. The partition function satisfies

$$L_n Z \equiv 0$$

for all $n\geq -1$.

These equations are the proposed Virasoro constraints for quantum cohomology, generalizing the Virasoro constraints for the KdV tau-function in the point case. The source presents this as a conjecture for Fano manifolds with only even-dimensional cohomology classes; a more general conjecture is attributed to Eguchi, Jiang and Xiong.