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Globally generated vector bundles on \(\mathbb P^n\) with \(c_1=3\). (English) Zbl 1279.14053
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, J. C. Sierra and L. Ugaglia study the case \(c_1 = 2\) in [J. Pure Appl. Algebra 213, No. 11, 2141–2146 (2009; Zbl 1166.14011)], L. Chiodera and 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 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.

MSC:
14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli
14H50 Plane and space curves
14N25 Varieties of low degree
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