Globally generated vector bundles on \(\mathbb P^n\) with \(c_1=3\) (Q2862555)

Globally generated vector bundles on a projective space \(\mathbb{P}^n\) (whose first Chern class \(c_1\) is always strictly positive) have been studied in some cases. The case \(c_1 = 1\) being trivial, \textit{J. C. Sierra} and \textit{L. Ugaglia} study the case \(c_1 = 2\) in [J. Pure Appl. Algebra 213, No. 11, 2141--2146 (2009; Zbl 1166.14011)], \textit{L. Chiodera} and \textit{P. Ellia} study the case of rank \(2\) bundles with \(c_1 \leq 5\) in [Rend. Ist. Mat. Univ. Trieste 44, 413--422 (2012; Zbl 1271.14020)], while \textit{S. Huh} in [Math. Nachr. 284, No. 11-12, 1453--1461 (2011; Zbl 1279.14014)] considered the case \(c_1 = 3\) (with rank \(2\)). This paper investigates the case \(c_1 = 3\) and gives a detailed description of such bundles on \(\mathbb{P}^2, \mathbb{P}^3,\mathbb{P}^4,\mathbb{P}^n\) in general.