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arXiv · 1409.7115

Homogeneity of cohomology classes associated with Koszul matrix factorizations

Alexander Polishchuk
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Abstract

In this work we prove the so called dimension property for the cohomological field theory associated with a homogeneous polynomial W with an isolated singularity, in the algebraic framework of arXiv:1105.2903. This amounts to showing that some cohomology classes on the Deligne-Mumford moduli spaces of stable curves, constructed using Fourier-Mukai type functors associated with matrix factorizations, live in prescribed dimension. The proof is based on a homogeneity result established in arXiv:math/0011032 for certain characteristic classes of Koszul matrix factorizations of 0. To reduce to this result we use the theory of Fourier-Mukai type functors involving matrix factorizations and the natural rational lattices in the relevant Hochschild homology spaces, as well as a version of Hodge-Riemann bilinear relations for Hochschild homology of matrix factorizations. Our approach also gives a proof of the dimension property for the cohomological field theories associated with some quasihomogeneous polynomials with an isolated singularity.

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Alexander Polishchuk. 2014-09-24. Homogeneity of cohomology classes associated with Koszul matrix factorizations. https://doi.org/10.1112/s0010437x16007557

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