Resumen de Frobenius manifolds and Virasoro constraints

B. Dubrovin, Y. Zhang

• 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.