@article {2008, title = {Frobenius Manifolds and Central Invariants for the Drinfeld - Sokolov Bihamiltonian Structures}, journal = {Adv. Math. 219 (2008) 780-837}, number = {arXiv.org;0710.3115}, year = {2008}, abstract = {The Drinfeld - Sokolov construction associates a hierarchy of bihamiltonian integrable systems with every untwisted affine Lie algebra. We compute the complete set of invariants of the related bihamiltonian structures with respect to the group of Miura type transformations.}, doi = {10.1016/j.aim.2008.06.009}, url = {http://hdl.handle.net/1963/2523}, author = {Boris Dubrovin and Liu Si-Qi and Zhang Youjin} } @article {1999, title = {Frobenius manifolds and Virasoro constraints}, journal = {Selecta Math. (N.S.) 5 (1999) 423-466}, number = {SISSA;84/98/FM}, year = {1999}, publisher = {Springer}, 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. Particularly, the genus $\\\\leq 1$ 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.}, doi = {10.1007/s000290050053}, url = {http://hdl.handle.net/1963/2883}, author = {Boris Dubrovin and Zhang Youjin} }