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Homological mirror symmetry for Milnor fibers of simple singularities

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arxiv 2004.07374 v2 pith:IRKEFEQN submitted 2020-04-15 math.AG math.SG

Yanki Lekili , Kazushi Ueda This is my paper · ORCID
classification math.AGmath.SG
keywords milnorsimplecohomologyfibersgreatergrouphomologicalmirror
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abstract

We prove homological mirror symmetry for Milnor fibers of simple singularities in dimensions greater than one, which are among the log Fano cases of Conjecture 1.5 in arXiv:1806.04345. The proof is based on a relation between matrix factorizations and Calabi--Yau completions. As an application, we give an explicit computation of the Hochschild cohomology group of the derived $n$-preprojective algebra of a Dynkin quiver for any $n \geq 1$, and the symplectic cohomology group of the Milnor fiber of any simple singularity in any dimension greater than one.

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  1. On holographic duals of certain isolated weighted Gorenstein cDV singularities

    hep-th 2024-12 reject novelty 5.0 of 10

    The paper claims, via mirror symmetry and a quiver search, that none of a listed set of cE6 and cE7 singularities admit crepant resolutions and hence lack N=1 quiver SCFT duals.

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