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

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 analogue of the Hirzebruch–Rieman...

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Bibliographic Details
Published in:Duke mathematical journal 2012-07, Vol.161 (10), p.1863-1926
Main Authors: Polishchuk, Alexander, Vaintrob, Arkady
Format: Article
Language:English
Subjects:
14A22
14B05
14H20
14J17
18E30
32S25
32Sxx
58Kxx
Derived categories
Noncommutative algebraic geometry [See also 16S38]
Singularities [See also 14E15
Surface and hypersurface singularities [See also 14J17]
triangulated categories
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Summary: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 analogue 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.
ISSN:0012-7094
1547-7398
DOI:10.1215/00127094-1645540