Chern characters and Hirzebruch-Riemann-Roch formula for matrix factorizations

Details Chern characters and Hirzebruch-Riemann-Roch formula for matrix factorizations Chern characters and Hirzebruch-Riemann-Roch formula for matrix factorizations

2010-02-10

arxiv.org/abs/1002.2116v2

Mathematics

Algebraic Geometry

45 pages, v2: added the generalized HRR theorem (Cardy condition) and new examples with the boundary-bulk maps

Scientific paper

We study the category of matrix factorizations for an isolated hypersurface singularity. We compute the canonical bilinear form on the Hochschild homology of this category. We find explicit expressions for the Chern character and the boundary-bulk maps and derive an analog of the Hirzebruch-Riemann-Roch formula for the Euler characteristic of the Hom-space between a pair of matrix factorizations. We also establish G-equivariant versions of these results.

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