The Derived Category of the Intersection of Four Quadrics

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.

arXiv commentAdded acknowledgement of NSF support

References in corpus (4)

• Semiorthogonal decomposition for algebraic varieties
• Derived categories of coherent sheaves
• Non-birational twisted derived equivalences in abelian GLSMs
• Rank Two Sheaves on K3 Surfaces: A Special Construction

Cited by in corpus (10)

• Decompactifications and Massless D-Branes in Hybrid Models
• Topological Strings on Non-Commutative Resolutions
• Algebraic cycles and intersections of three quadrics
• ACM bundles on cubic fourfolds containing a plane
• GLSM's, gerbes, and Kuznetsov's homological projective duality
• On Clifford double mirrors of toric complete intersections
• Birational maps between Calabi-Yau manifolds associated to webs of quadrics
• Vector Bundles on non-Kähler elliptic principal bundles
• General Mirror Pairs for Gauged Linear Sigma Models
• On derived equivalence of general Clifford double mirrors