The Clifford-algebra resolution conjecture for the Calabi–Yau double cover

Let XX be the base of the Calabi–Yau double cover YY, let Cl0Cl_{0} be the even part of the sheaf of Clifford algebras obtained from the quadratic GLSM superpotential, and write D(Y):=DbCoh(Y)D(Y):=D^{b}\operatorname{Coh}(Y). Clifford-algebra resolution conjecture.

D(X,Cl0)D(Y).D(X,Cl_{0})\cong D(Y).

This proposes that the Clifford-module category gives a non-commutative resolution equivalent to the derived category of the double cover, fitting the expected homological mirror-symmetry picture; the source notes that the corresponding Fukaya category for the singular mirror is not yet defined.

Sources & referencesView supporting material

Primary source

Tsung-Ju Lee, Bong H. Lian and Mauricio Romo, “Non-commutative resolutions as mirrors of singular Calabi–Yau varieties”, arXiv:2307.02038 (2023).

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