Article Dans Une Revue Commentarii Mathematici Helvetici Année : 2011

Rational connectedness modulo the non-nef locus

Gianluca Pacienza
  • Fonction : Auteur

Résumé

It is well known that a smooth projective Fano variety is rationally connected. Recently Zhang [Z2] (and later Hacon and McKernan [HM] as a special case of their work on the Shokurov RC-conjecture) proved that the same conclusion holds for a klt pair (X,\Delta) such that -(K_X+\Delta) 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,\Delta) such that -(K_X+\Delta) is big is rationally connected modulo the non-nef locus of -(K_X+\Delta) . This result is a consequence of a more general structure theorem for arbitrary pairs (X,\Delta) with -(K_X+\Delta) pseff.

Dates et versions

hal-05506691 , version 1 (12-02-2026)

Identifiants

Citer

Amaël Broustet, Gianluca Pacienza. Rational connectedness modulo the non-nef locus. Commentarii Mathematici Helvetici, 2011, 86 (3), pp.593-607. ⟨10.4171/CMH/235⟩. ⟨hal-05506691⟩
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