Singular Hochschild cohomology and reconstruction of singularities

Abstract: We show that under a mild regularity assumption, singular Hochschild cohomology (also known as Tate-Hochschild cohomology) identifies with Hochschild cohomology of the (dg enhanced) singularity category. In joint work with Zheng Hua, we apply this to the reconstruction of a (complete isolated) compound Du Val singularity from its contraction algebra together with the additional datum of a class in its zeroth Hochschild homology. This provides some evidence towards a conjecture by Donovan-Wemyss according to which the contraction algebra alone determines such a singularity.

algebraic geometrydifferential geometrygeometric topologysymplectic geometry

Audience: researchers in the topic

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