Nicolas Addington

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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)
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