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

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

2000-06-26

arxiv.org/abs/math/0006193v2

IMRN, 2001, No 23, 1243-1264

Mathematics

Algebraic Geometry

17 pages, LaTeX, a few local improvements made

Scientific paper

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.

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