Quantum periods - I. Semi-infinite variations of Hodge structures.

Serguei Barannikov (1)

1 DMA - Département de Mathématiques et Applications - ENS Paris

We introduce a generalization of variations of Hodge structures living over moduli spaces of non-commutative deformations of complex manifolds. Hodge structure associated with a point of such moduli space is an element of Sato type grassmanian of semi-infinite subspaces in H^*(X,C)[[h^{-1},h]]. Periods associated with such semi-infinite Hodge structures serve in order to extend mirror symmetry relations in dimensions greater then three. (arXiv:math/0006193)

Mots clés: nc-Hodge theory; mirror symmetry; Calabi-Yau manifolds; A-infinity categories

Domaines: Géométrie algébrique [math.AG]; Physique des Hautes Energies - Théorie [hep-th]

Serguei Barannikov. Quantum periods - I. Semi-infinite variations of Hodge structures.. International Mathematics Research Notices, 2000, 2001 (23), pp.1243-1264. ⟨10.1155/S1073792801000599⟩. ⟨hal-00430505⟩