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Quantum periods. I: Semi-infinite variations of Hodge structures. (English) Zbl 1074.14510
Summary: We introduce a generalization of variations of Hodge structures living over moduli spaces of noncommutative deformations of complex manifolds. Hodge structure associated with a point of such moduli space is an element of Sato type Grassmannian of semi-infinite subspaces in \(H^{*} (X,\mathbb{C})[[h^{\pm 1}]]\). Periods associated with such semi-infinite Hodge structures enter into mirror symmetry formulas in dimensions greater then three.

MSC:
14D07 Variation of Hodge structures (algebro-geometric aspects)
14A22 Noncommutative algebraic geometry
32G20 Period matrices, variation of Hodge structure; degenerations
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
32J25 Transcendental methods of algebraic geometry (complex-analytic aspects)
32Q25 Calabi-Yau theory (complex-analytic aspects)
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