Displaying similar documents to “On del Pezzo fibrations”

Subsheaves of the cotangent bundle

Paolo Cascini (2006)

Open Mathematics

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For any smooth projective variety, we study a birational invariant, defined by Campana which depends on the Kodaira dimension of the subsheaves of the cotangent bundle of the variety and its exterior powers. We provide new bounds for a related invariant in any dimension and in particular we show that it is equal to the Kodaira dimension of the variety, in dimension up to 4, if this is not negative.

Effective nonvanishing, effective global generation

Mark Andrea A. De Cataldo (1998)

Annales de l'institut Fourier

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We prove a multiple-points higher-jets nonvanishing theorem by the use of local Seshadri constants. Applications are given to effectivity problems such as constructing rational and birational maps into Grassmannians, and the global generation of vector bundles.