Syzygies of the secant variety of a curve

TL;DR

This paper proves that the secant variety of a linearly normal smooth curve with degree at least 2g+3 is arithmetically Cohen-Macaulay and investigates its graded Betti numbers.

Contribution

It establishes the Cohen-Macaulay property for secant varieties of certain curves and analyzes their graded Betti numbers, advancing understanding of their algebraic structure.

Findings

Secant variety is arithmetically Cohen-Macaulay for degree ≥ 2g+3.

Provides detailed information on the graded Betti numbers.

Enhances knowledge of algebraic properties of secant varieties.

Abstract

We show that the secant variety of a linearly normal smooth curve of degree at least 2g+3 is arithmetically Cohen-Macaulay, and we use this information to study the graded Betti numbers of the secant variety.