Globally Generated Vector Bundles on P^n with c_1=3

TL;DR

This paper classifies globally generated vector bundles on projective space P^n with first Chern class 3, extending previous classifications for specific ranks and dimensions, and filling a gap in the understanding of such bundles.

Contribution

It provides a classification of globally generated vector bundles on P^n with c_1=3 for all n ≠ 3, complementing prior work on special cases and ranks.

Findings

Classification for n ≠ 3 completed

Connections to previous classifications for specific ranks

Extends understanding of vector bundles with c_1=3

Abstract

One classifies the globally generated vector bundles on P^n (n \not = 3) with the first Chern class c_1 = 3. The case n = 3 is treated in arXiv:1202.5988 [math.AG]. The case c_1 = 2 was treated by J.C. Sierra and L. Ugaglia (see References), the case c_1 = 3, rank = 2 is settled by S. Huh (see References), the case rank = 2, c_1 \le 5 is studied by L. Chiodera and Ph. Ellia (see References).