On Generalised Abundance, I

TL;DR

This paper explores deep conjectures in algebraic geometry, linking the Nonvanishing, Abundance, and Semiampleness Conjectures for nef line bundles on K-trivial varieties, aiming to unify understanding of their interrelations.

Contribution

It establishes a surprising connection between key conjectures in algebraic geometry, potentially advancing the understanding of the structure of nef line bundles on K-trivial varieties.

Findings

Identifies a link between the Nonvanishing and Abundance Conjectures.

Proposes a unified perspective on the Semiampleness Conjecture.

Suggests new approaches to longstanding conjectures in algebraic geometry.

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.