Pushing forward matrix factorisations

Abstract

We describe the pushforward of a matrix factorisation along a ring morphism in terms of an idempotent defined using relative Atiyah classes, and use this construction to study the convolution of kernels defining integral functors between categories of matrix factorisations. We give an elementary proof of a formula for the Chern character of the convolution generalising the Hirzebruch-Riemann-Roch formula of Polishchuk and Vaintrob.

43 pages, comments welcome

References in corpus (3)

• Duality and defects in rational conformal field theory
• B-type defects in Landau-Ginzburg models
• Rigidity and defect actions in Landau-Ginzburg models

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