2020/02/17 by Cristian Anghel, Iustin Coandă, Anghel, Cristian +3
Mathematics · Physics and Astronomy · #14H50 #14J60 #14N25 #Advanced Differential Geometry Research #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2002.07167
openalex publication_date 2020/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We complete the classification of globally generated vector bundles with\nsmall c1 on projective spaces by treating the case c1 = 5 on\n\ℙn, n \≥ 4 (the case c1 \≤ 3 has been considered by Sierra\nand Ugaglia, while the cases c1 = 4 on any projective space and c1 = 5 on\n\ℙ2 and \ℙ3 have been studied in two of our previous\npapers). It turns out that there are very few indecomposable bundles of this\nkind: besides some obvious examples there are, roughly speaking, only the\n(first twist of the) rank 5 vector bundle which is the middle term of the monad\ndefining the Horrocks bundle of rank 3 on \ℙ5, and its restriction\nto \ℙ4. We recall, in an appendix, from our preprint\n[arXiv:1805.11336], the main results allowing the classification of globally\ngenerated vector bundles with c1 = 5 on \ℙ3. Since there are many\nsuch bundles, a large part of the main body of the paper is occupied with the\nproof of the fact that, except for the simplest ones, they do not extend to\n\ℙ4 as globally generated vector bundles.\n