Non-commutative Hodge structures: Towards matching categorical and geometric examples

Details Non-commutative Hodge structures: Towards matching categorical and geometric examples Non-commutative Hodge structures: Towards matching categorical and geometric examples

2011-07-15

arxiv.org/abs/1107.3156v1

Mathematics

Algebraic Geometry

51 pages

Scientific paper

The subject of the present work is the "de Rham part" of non-commutative Hodge structures on the periodic cyclic homology of differential graded algebras and categories. We discuss explicit formulas for the corresponding connection on the periodic cyclic homology viewed as a bundle over the punctured formal disk. Our main result says that for the category of matrix factorizations of a polynomial the formulas reproduce the connection on the associated twisted de Rham complex that is considered in the geometric approach to the Hodge theory of isolated singularities.

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