The Weil Decoration of the Horrocks-Mumford Bundle

TL;DR

This paper generalizes the relationship between reflexive sheaves and Weil divisors to higher ranks, introducing Weil decorations, and applies this to define a new generalization of the Horrocks-Mumford bundle.

Contribution

It extends the classical correspondence to higher rank sheaves and introduces Weil decorations, leading to a novel generalization of the Horrocks-Mumford bundle.

Findings

Established a generalized relation between reflexive sheaves and Weil divisors.

Defined and studied a new class of bundles generalizing Horrocks-Mumford.

Provided foundational tools for further exploration of higher rank sheaves.

Abstract

For a normal algebraic variety we generalise the relation between reflexive rank one sheaves and Weil divisors to reflexive sheaves of arbitrary rank and so-called Weil decorations. As an application, we define and study a natural generalisation of the celebrated Horrocks-Mumford bundle.