Gotzmann's persistence theorem for finite modules

TL;DR

This paper generalizes Gotzmann's persistence theorem to finite modules with constant Hilbert polynomial, revealing that the embedding of a Quot scheme of points into a Grassmannian is defined by a single Fitting ideal.

Contribution

It extends Gotzmann's theorem to modules and shows that the Quot scheme embedding is characterized by one Fitting ideal, simplifying its algebraic description.

Findings

Generalized Gotzmann's persistence theorem for modules

Identified the embedding of Quot schemes via a single Fitting ideal

Simplified the algebraic description of Quot scheme embeddings

Abstract

We prove a generalization of Gotzmann's persistence theorem in the case of modules with constant Hilbert polynomial. As a consequence, we show that the defining equations that give the embedding of a Quot scheme of points into a Grassmannian are given by a single Fitting ideal.