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arXiv · 0904.1764

The Derived Category of the Intersection of Four Quadrics

Nicolas Addington
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Abstract

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 3-folds predicted by Gross. This differs from Kuznetsov's result in that our construction is geometric and avoids non-commutative varieties.

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Nicolas Addington. 2009-11-11. The Derived Category of the Intersection of Four Quadrics. https://arxiv.org/abs/0904.1764

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