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ISBN: 9781470428389 1470428385 Year: 2018 Publisher: Providence American Mathematical Society
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Vector bundles. --- Geometry, Projective. --- Projective spaces. --- Chern classes. --- Fibrés vectoriels. --- Géométrie projective. --- Chern, Classes de. --- Espaces projectifs. --- Vector bundles --- Geometry, Projective --- Projective spaces --- Chern classes --- Chern characteristic classes --- Chern's characteristic classes --- Chern's classes --- Classes, Chern --- Spaces, Projective --- Projective geometry --- Fibrés vectoriels --- Géométrie projective --- Espaces projectifs --- Classes de Chern --- Characteristic classes --- Geometry, Modern --- Fiber spaces (Mathematics)
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ISBN: 1470444135 Year: 2018 Publisher: Providence, RI : American Mathematical Society,
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The authors provide a complete classification of globally generated vector bundles with first Chern class c_1 leq 5 one the projective plane and with c_1 leq 4 on the projective n-space for n geq 3. This reproves and extends, in a systematic manner, previous results obtained for c_1 leq 2 by Sierra and Ugaglia [J. Pure Appl. Algebra 213 (2009), 2141-2146], and for c_1 = 3 by Anghel and Manolache [Math. Nachr. 286 (2013), 1407-1423] and, independently, by Sierra and Ugaglia [J. Pure Appl. Algebra 218 (2014), 174-180]. It turns out that the case c_1 = 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 (conveniently twisted). The authors also propose a conjecture concerning the classification of globally generated vector bundles with c_1 leq n - 1 on the projective n-space. They verify the conjecture for n leq 5.
Vector bundles. --- Geometry, Projective. --- Projective spaces. --- Chern classes.
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