Resolution of the symmetric algebra of a finite base locus

TL;DR

This paper presents a method to explicitly resolve the symmetric algebra of a zero-dimensional scheme's ideal sheaf using known resolutions and the Eagon-Northcott complex, advancing algebraic geometry techniques.

Contribution

It introduces a new locally free resolution of the symmetric algebra for zero-dimensional schemes, linking it to the ideal's resolution and the Eagon-Northcott complex.

Findings

Provides an explicit locally free resolution of the symmetric algebra.

Connects the resolution to the ideal's resolution and the Eagon-Northcott complex.

Enhances understanding of the structure of symmetric algebras in algebraic geometry.

Abstract

We provide a locally free resolution of the projectivized symmetric algebra of the ideal sheaf of a zero-dimensional scheme defined by n + 1 equations in an n-dimensional variety. The resolution is given in terms of the resolution of the ideal itself and of the Eagon-Northcott complex of the Koszul hull.