Asymptotics of discrete Okounkov bodies and thresholds

TL;DR

This paper explores the asymptotic behavior of discrete Okounkov bodies and higher-dimensional Weierstrass gaps, providing new insights into stability and log canonical thresholds in algebraic geometry.

Contribution

It introduces the study of discrete Okounkov bodies and higher-dimensional Weierstrass gaps, linking them to asymptotic stability and threshold analysis.

Findings

Established foundational properties of discrete Okounkov bodies.

Connected higher-dimensional Weierstrass gaps to asymptotic invariants.

Applied these concepts to analyze stability and log canonical thresholds.

Abstract

This article initiates the study of discrete Okounkov bodies and higher-dimensional Weierstrass gap phenomena, with applications to asymptotic analysis of stability and global log canonical thresholds.