Geometry of the Sasakura bundle

TL;DR

This paper explores the geometric properties of the Sasakura bundle, a recent and notable vector bundle on projective spaces, and discusses its role in classifying certain sheaves with low first Chern class.

Contribution

It consolidates scattered literature on the Sasakura bundle and examines its significance in the classification of globally generated sheaves with small first Chern class.

Findings

Connections between the Sasakura bundle and specific surfaces in projective space

Its role in the classification of globally generated sheaves with c1 ≤ 4

Insights into the geometry of the bundle

Abstract

The Sasakura bundle is a relatively recent appearance in the world of remarkable vector bundles on projective spaces. In fact, it is connected with some surfaces in $\mathbb P^4$ which missed in early classification papers. The aim of this note is to present various, scattered in the literature, aspects concerning the geometry of this bundle. The last part will be devoted to the place of this bundle in the classification of globally generated locally free sheaves with $c_1 \leq 4$ on $\mathbb P^n$ in a joint paper with I. Coanda and N. Manolache.