Derived categories and rationality of conic bundles

Details Derived categories and rationality of conic bundles Derived categories and rationality of conic bundles

2010-10-12

arxiv.org/abs/1010.2417v3

Mathematics

Algebraic Geometry

New version; now also the case of cubic degeneration in P^2 is described in detail. 23 Pages

Scientific paper

We show that a standard conic bundle over a minimal rational surface is rational and its Jacobian splits as the direct sum of Jacobians of curves if and only if its derived category admits a semiorthogonal decomposition by exceptional objects and the derived categories of those curves. Moreover, such a decomposition gives the splitting of the intermediate Jacobian also when the surface is not minimal.

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