Duke Mathematical Journal

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

Alexander Polishchuk and Arkady Vaintrob

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Abstract

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.

Article information

Source
Duke Math. J., Volume 161, Number 10 (2012), 1863-1926.

Dates
First available in Project Euclid: 27 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1340801626

Digital Object Identifier
doi:10.1215/00127094-1645540

Mathematical Reviews number (MathSciNet)
MR2954619

Zentralblatt MATH identifier
1249.14001

Subjects
Primary: 14A22: Noncommutative algebraic geometry [See also 16S38]
Secondary: 14B05: Singularities [See also 14E15, 14H20, 14J17, 32Sxx, 58Kxx] 32S25: Surface and hypersurface singularities [See also 14J17] 18E30: Derived categories, triangulated categories

Citation

Polishchuk, Alexander; Vaintrob, Arkady. Chern characters and Hirzebruch–Riemann–Roch formula for matrix factorizations. Duke Math. J. 161 (2012), no. 10, 1863--1926. doi:10.1215/00127094-1645540. https://projecteuclid.org/euclid.dmj/1340801626


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