Asymptotic syzygies of secant varieties of curves

TL;DR

This paper proves that the minimal free resolution of secant varieties of curves becomes asymptotically pure and that their Betti numbers follow a normal distribution as the variety's parameters grow.

Contribution

It introduces the concept of asymptotic purity for minimal free resolutions of secant varieties and establishes the normal distribution convergence of Betti numbers.

Findings

Minimal free resolution of secant varieties is asymptotically pure.

Betti numbers of secant varieties converge to a normal distribution.

Provides new insights into the algebraic and probabilistic structure of secant varieties.

Abstract

We prove that the minimal free resolution of the secant variety of a curve is asymptotically pure. As a corollary, we show that the Betti numbers of converge to a normal distribution.