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

By Alexander Polishchuk, A. Vaintrob. 2010

121 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3444ad924864c5cf445d48a34ad0956dfdc22e37

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In Geometry and Topology

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Citations in the corpus

A category of kernels for equivariant factorizations and its implications for Hodge theory (2011, background): “ompute the extended Hochschild cohomology of (X,G,w) when Xis aﬃne, Gis a ﬁnite extension of Gm, and wis semi-homogeneous regular function of non-torsion degree. The computation is along the lines of [PV12]. Theorem 1.2. Let Gact linearly on An and let w∈Γ(An,O An(χ))G. Assume that the kernel of χ, ”
Matrix factorizations and Cohomological Field Theories (2011, background): “.2. The specialization of Hat t= 1 is the algebra C[H0,0,u]/(ud−1,xu,xy−((ζ•)∗x,y)ud−2), where x,y∈ H0,0 = H(w)Z/d. Indeed, this follows easily from the fact that e(0) has zero component in H0,0 (see [53]). In the case when d= nthe category of Gm-equivariant matrix factorizations of w is equivalent ”