Abstract.
For an arbitrary Frobenius manifold, a system of Virasoro constraints is constructed. In the semisimple case these constraints are proved to hold true in the genus one approximation. In particular, the genus ≤ 1 Virasoro conjecture of T. Eguchi, K. Hori, M. Jinzenji, and C.-S. Xiong and of S. Katz is proved for smooth projective varieties having semisimple quantum cohomology.
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Dubrovin, B., Zhang, Y. Frobenius manifolds and Virasoro constraints. Sel. math., New ser. 5, 423–466 (1999). https://doi.org/10.1007/s000290050053
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DOI: https://doi.org/10.1007/s000290050053