{"paper":{"title":"Morphisms and faces of pseudo-effective cones","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Brian Lehmann, Mihai Fulger","submitted_at":"2016-01-13T16:58:15Z","abstract_excerpt":"Let $\\pi: X \\to Y$ be a morphism of projective varieties and suppose that $\\alpha$ is a pseudo-effective numerical cycle class satisfying $\\pi_*\\alpha = 0$. A conjecture of Debarre, Jiang, and Voisin predicts that $\\alpha$ is a limit of classes of effective cycles contracted by $\\pi$. We establish new cases of the conjecture for higher codimension cycles. In particular we prove a strong version when $X$ is a fourfold and $\\pi$ has relative dimension one."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.03314","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}