On Generalised Abundance, I

Abstract

The goal of this paper is to make a surprising connection between several central conjectures in algebraic geometry: the Nonvanishing Conjecture, the Abundance Conjecture, and the Semiampleness Conjecture for nef line bundles on K-trivial varieties.

References in corpus (1)

• Quelques remarques sur la décomposition de Zariski divisorielle sur les variétés dont la première classe de Chern est nulle

Cited by in corpus (12)

• On the existence of minimal models for log canonical pairs
• The Nonvanishing problem for varieties with nef anticanonical bundle
• Existence of flips for generalized lc pairs
• Strictly nef divisors on K-trivial fourfolds
• Strictly nef divisors and some remarks on a conjecture of Serrano
• Strictly nef divisors on singular threefolds
• Minimal model program for normal pairs along log canonical locus
• Two Non-Vanishing results concerning the Anti-Canonical Bundle
• Abundance for uniruled pairs which are not rationally connected
• Strictly nef vector bundles and characterizations of ${\mathbb{P}}^n$
• Semipositive line bundles and (1,1)-classes
• On the existence of rational curves on projective hyperkähler fourfolds