# On degenerate sections of vector bundles

## TL;DR

This paper studies the geometric structure of sections of vector bundles on projective schemes that vanish in unexpectedly high dimensions, revealing their minimal degree subscheme structure after sufficient twisting.

## Contribution

It provides a detailed description of the locus of such sections and its limit in the Grothendieck ring, advancing understanding of vector bundle sections and their degeneracies.

## Key findings

- Maximal components consist of sections vanishing along minimal degree subschemes
- A high enough twist ensures the locus has a predictable structure
- The limit in the Grothendieck ring can be explicitly described

## Abstract

We consider the locus of sections of a vector bundle on a projective scheme that vanish in higher dimension than expected. We show that after applying a high enough twist, any maximal component of this locus consists entirely of sections vanishing along a subscheme of minimal degree. In fact, we will give a more refined description of this locus, which will allow us to deduce its limit in the Grothendieck ring of varieties.