Remarks on the cone of divisors

TL;DR

This paper investigates the structure of divisor cones in algebraic geometry, providing new theorems on their decompositions and introducing numerical linear systems to simplify Zariski decomposition arguments.

Contribution

It presents two theorems on locally finite decompositions of divisor cones and introduces numerical linear systems to streamline Zariski decomposition analysis.

Findings

Proved theorems on cone decompositions related to canonical and minimal models

Introduced numerical linear systems for simplifying Zariski decompositions

Enhanced understanding of the structure of divisor cones in algebraic geometry

Abstract

We prove two theorems on the locally finite decompositions of the cones of divisors by the cones which correspond to canonical and minimal models. We introduce the concept of the numerical linear systems in order to simplify the argument on the Zariski decompositions.