Gotzmann regularity for globally generated coherent sheaves

TL;DR

This paper extends Gotzmann's Regularity Theorem to globally generated coherent sheaves on projective space and applies it to bound characteristic classes, enhancing understanding of their geometric properties.

Contribution

It generalizes Gotzmann's Regularity Theorem to a broader class of sheaves and extends the explicit construction to the Quot scheme.

Findings

Established Gotzmann's Regularity Theorem for globally generated sheaves

Extended Gotzmann's construction to the Quot scheme

Bound the second Chern class in terms of the first for rank 2 sheaves

Abstract

In this paper, Gotzmann's Regularity Theorem is established for globally generated coherent sheaves on projective space. This is used to extend Gotzmann's explicit construction to the Quot scheme. The Gotzmann representation is applied to bound the second Chern class of a rank 2 globally generated coherent sheaf in terms of the first Chern class.