Morphisms and faces of pseudo‐effective cones. Issue 4 (7th March 2016) - Fulger, Mihai; Lehmann, Brian
Abstract : Letπ : X → Y be a morphism of projective varieties and suppose thatα is a pseudo‐effective numerical cycle class satisfyingπ * α = 0 . A conjecture of Debarre, Jiang, and Voisin predicts thatα is a limit of classes of effective cycles contracted byπ . We establish new cases of the conjecture for higher codimension cycles. In particular, we prove a strong version whenX is a fourfold andπ has relative dimension 1.