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The derived category of a general complete intersection of four quadrics in P 2n−1 has a semi-orthogonal decomposition O(−2n + 9),. .. , O(−1), O, D, where D is the derived category of twisted sheaves on a certain non-algebraic complex 3-fold coming from a moduli problem. In particular, when n = 4 we obtain a (twisted) derived equivalence of Calabi-Yau… (More)
We define sheaves on a singular quadric Q that generalize the spinor bundles on smooth quadrics, using matrix factorizations of the equation of Q. We study the first properties of these spinor sheaves, prove an analogue of Horrocks' criterion, and show that they are semi-stable, and indeed stable in some cases.
We give a new proof of the ‘Pfaffian-Grassmannian’ derived equivalence between certain pairs of non-birational Calabi–Yau threefolds. Our proof follows the physical constructions of Hori and Tong, and we factor the equivalence into three steps by passing through some intermediate categories of (global) matrix factorizations. The first step is global Knörrer… (More)
We develop a method for recovering arbitrary graphs, a generalization of the star–k method that avoids spurious parameters. They key is to recognize that the inverse problem amounts to undoing the Schur complement and to analyze the residue term − BC −1 B .