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Derived categories and rationality of conic bundles

Derived categories and rationality of conic bundles

Update: 2011-07-01
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In this talk I present a joint work with Marcello Bernardara where we show that a standard conic bundle on a rational minimal surface is rational if and only if its derived category admits a semiothogonal decomposition via derived categories of smooth projective curves and exceptional objects. In particular, even if the surface is not minimal, such a decomposition allows to reconstruct the intermediate Jacobian as the direct sum of the Jacobian of those curves.
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Derived categories and rationality of conic bundles

Derived categories and rationality of conic bundles

Cambridge University