Quantum periods - I. Semi-infinite variations of Hodge structures
Algebraic Geometry
2021-07-14 v2 High Energy Physics - Theory
Commutative Algebra
Quantum Algebra
Abstract
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.
Keywords
Cite
@article{arxiv.math/0006193,
title = {Quantum periods - I. Semi-infinite variations of Hodge structures},
author = {S. Barannikov},
journal= {arXiv preprint arXiv:math/0006193},
year = {2021}
}
Comments
17 pages, LaTeX, a few local improvements made