Derived categories of cubic and V14 threefolds

Details Derived categories of cubic and V14 threefolds Derived categories of cubic and V14 threefolds

2003-03-04

arxiv.org/abs/math/0303037v1

Mathematics

Algebraic Geometry

24 pages, dedicated to the memory of Andrei Nikolaevich Tyurin

Scientific paper

We show that the projectivization of the exceptional rank 2 vector bundle on an arbitrary smooth V14 Fano threefold after a certain natural flop turns into the projectivization of an instanton vector bundle on a smooth cubic threefold. And vice versa, starting from a smooth cubic threefold with an instanton vector bundle of charge 2 on it we reconstruct V14 threefold. Relying on the geometric properties of the above correspondence we prove that the orthogonals to the exceptional pairs in the bounded derived categories of coherent sheaves on a smooth V14 threefold and on the corresponding cubic threefold are equivalent as triangulated categories.

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