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 such that 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 such that is big is rationally connected modulo the non-nef locus of . This result is a consequence of a more general structure theorem for arbitrary pairs with pseff.
Cite this article
Amaël Broustet, Gianluca Pacienza, Rational connectedness modulo the non-nef locus. Comment. Math. Helv. 86 (2011), no. 3, pp. 593–607DOI 10.4171/CMH/235