Asymptotic Weights of Syzygies of Toric Varieties

TL;DR

This paper provides a detailed asymptotic analysis of the weights in syzygies of toric varieties, showing stabilization of weights as the embedding becomes more positive, with explicit descriptions.

Contribution

It offers a precise asymptotic characterization of syzygy weights in toric varieties, including explicit stabilization patterns as positivity increases.

Findings

Weights stabilize to a fixed shape with increased positivity

Explicit description of the stabilized weights

Asymptotic behavior of syzygy weights clarified

Abstract

The purpose of the paper is to give a sharp asymptotic description of the weights that appear in the syzygies of a toric variety. We prove that as the positivity of the embedding increases, in any strand of syzygies, torus weights after normalization stabilize to the same fixed shape that we explicitly specify.