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Derived categories and rationality of conic bundles

Published online by Cambridge University Press:  07 October 2013

Marcello Bernardara
Affiliation:
Univeristät Duisburg–Essen, Fakultät für Mathematik. Universitätstr. 2, 45117 Essen, Germany email [email protected] Institut de Mathématiques de Toulouse (IMT), 118 route de Narbonne, Université Paul Sabatier, F-31062 Toulouse Cedex 9, France email [email protected]
Michele Bolognesi
Affiliation:
IRMAR, Université de Rennes 1, 263 Av. Général Leclerc, Bat. 22, 35042 Rennes Cedex, France email [email protected]
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Abstract

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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.

Type
Research Article
Copyright
© The Author(s) 2013 

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