Globally Generated Vector Bundles on P^n with c_1=4

TL;DR

This paper classifies all globally generated vector bundles on projective n-space with first Chern class 4, extending previous classifications for lower Chern classes and revealing increased complexity especially in three-dimensional cases.

Contribution

It provides a comprehensive classification of globally generated vector bundles with c_1=4, including new examples like the Sasakura bundle, and improves upon prior results for lower Chern classes.

Findings

Classification of bundles with c_1=4 on P^n

Identification of the Sasakura bundle in the classification

Increased complexity in the case of P^3

Abstract

We classify globally generated vector bundles on the projective n-space with first Chern class = 4. This extends previous results for first Chern class at most 3, namely for 2 of Sierra and Ugaglia [J. Pure Appl. Algebra 213 (2009), 2141-2146] and for 3 of Anghel and Manolache [arXiv:1202.6261] and, independently, of Sierra and Ugaglia [arXiv:1203.0185]. It turns out that the case first Chern class = 4 is much more involved than the previous cases, especially on the projective 3-space. Among the bundles appearing in our classification one can find the Sasakura rank 3 vector bundle on the projective 4-space (suitably twisted). In the new version Sections 1, 2, 4. 5, 6 and 7 have been rewritten and some arguments and the presentation have been, hopefully, improved.