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Pré-Publication, Document De Travail Année : 2009

Rational connectedness modulo the Non-nef locus

Résumé

It is well known that a smooth projective Fano variety is rationally connected. Recently Zhang (and later Hacon and McKernan as a special case of their work on the Shokurov RC-conjecture) proved that the same conclusion holds for a klt pair $(X,\D)$ such that $-(K_X+\D)$ is big and nef. We prove here a natural generalization of the above result by dropping the nefness assumption. Namely we show that a klt pair $(X,\D)$ such that $-(K_X+\D)$ is big is rationally connected modulo the non-nef locus of $-(K_X+\D)$. This result is a consequence of a more general structure theorem for arbitrary pairs $(X,\D)$ with $-(K_X+\D)$ pseff.
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Dates et versions

hal-00356588 , version 1 (27-01-2009)

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Amaël Broustet, Gianluca Pacienza. Rational connectedness modulo the Non-nef locus. 2009. ⟨hal-00356588⟩
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