Abstract:Given a smooth 3-fold Y , a line bundle L → Y , and a section s of L such that the vanishing locus of s is a normal crossings surface X with graph-like singular locus, we present a way to reconstruct the singularity category of X as a homotopy limit of several copies of the category of matrix factorizations of xyz : A 3 → A 1 (the mirror to the Fukaya category of the pair of pants). This extends our previous result for the case where L is trivialized. The key technique is the classification of non-two-periodic… Show more
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