Derived category of V₁₂ Fano threefolds

2003/10/01 by Alexander Kuznetsov, Kuznetsov, Alexander
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.AG

paper · pdf · doi:10.48550/arxiv.math/0310008

11 pages

arxiv created 2003/10/01 · arxiv updated 2009/12/01

Abstract

A V₁₂ Fano threefold is a smooth Fano threefold X of index 1 with Pic X = Z and (-K_X)³=12. We show that the bounded derived category of coherent sheaves on any V₁₂ threefold X admits a semiorthogonal decomposition consisting of two exceptional bundles and of the derived category of a curve of genus 7. As an application we show that the Fano surface of X (the surface parameterizing conics on X) is canonically isomorphic to the symmetric square of the associated genus 7 curve.

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