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arXiv:1010.2417 [math.AG]AbstractReferencesReviewsResources

Derived categories and rationality of conic bundles

Marcello Bernardara, Michele Bolognesi

Published 2010-10-12, updated 2012-12-11Version 4

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.

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