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Derived category of V_{12} Fano threefolds

Alexander Kuznetsov
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Abstract

A V_{12} 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 V_{12} 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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Alexander Kuznetsov. 2003-10-01. Derived category of V_{12} Fano threefolds. https://arxiv.org/abs/math/0310008

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