Cones and Asymptotic Invariants of Multigraded Systems of Ideals

TL;DR

This paper introduces cone structures and asymptotic invariants for multigraded systems of ideals, revealing that convexity is the primary formal restriction on such structures.

Contribution

It formalizes cone structures and asymptotic invariants for multigraded ideals, highlighting convexity as the main constraint.

Findings

Convexity is the only formal restriction on cone structures.

Introduces a framework for asymptotic invariants in multigraded systems.

Provides a mathematical foundation for understanding multigraded ideal systems.

Abstract

We define cone structures and asymptotic invariants for multigraded systems of ideals, and show that essentially the only restrictions on such structures is convexity, which is imposed formally.