Morphisms and faces of pseudo‐effective cones. Issue 4 (7th March 2016)

• Record Type: Journal Article
• Authors: Fulger, Mihai; Lehmann, Brian
• Is Part Of: Proceedings of the London Mathematical Society. Volume 112:Issue 4(2016:Apr.)
• Page Start: 651
• Page End: 676
• Publication Date: 2016-03-07
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1112/plms/pdw008
• Languages: English
• ISSNs: 0024-6115

Abstract

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.