Pseudo-effective classes and pushforwards

2013/01/17 by Olivier Debarre, Zhi Jiang, Debarre, O. +3 · 1 citation
Mathematics · #14C25 #14C30 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1301.4002

openalex publication_date 2013/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

Given a morphism between complex projective varieties, we make several conjectures on the relations between the set of pseudo-effective (co)homology classes which are annihilated by pushforward and the set of classes of varieties contracted by the morphism. We prove these conjectures for classes of curves or divisors. We also prove that one of these conjectures implies Grothendieck's generalized Hodge conjecture for varieties with Hodge coniveau at least 1.

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• Isoresidual fibrations and the birational geometry of moduli of pointed stable curves

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