Derived category of V_{12} Fano threefolds
Algebraic Geometry
2007-05-23 v1
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.
Cite
@article{arxiv.math/0310008,
title = {Derived category of V_{12} Fano threefolds},
author = {Alexander Kuznetsov},
journal= {arXiv preprint arXiv:math/0310008},
year = {2007}
}
Comments
11 pages