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Globally generated vector bundles with small
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 Sie...
Autores principales: | , , |
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Lenguaje: | eng |
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American Mathematical Society
2018
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Acceso en línea: | http://cds.cern.ch/record/2635384 |
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author | Anghel, Cristian Coandă, Iustin Manolache, Nicolae |
author_facet | Anghel, Cristian Coandă, Iustin Manolache, Nicolae |
author_sort | Anghel, Cristian |
collection | CERN |
description | 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. |
id | cern-2635384 |
institution | Organización Europea para la Investigación Nuclear |
language | eng |
publishDate | 2018 |
publisher | American Mathematical Society |
record_format | invenio |
spelling | cern-26353842021-04-21T18:43:47Zhttp://cds.cern.ch/record/2635384engAnghel, CristianCoandă, IustinManolache, NicolaeGlobally generated vector bundles with smallMathematical Physics and MathematicsThe 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.American Mathematical Societyoai:cds.cern.ch:26353842018 |
spellingShingle | Mathematical Physics and Mathematics Anghel, Cristian Coandă, Iustin Manolache, Nicolae Globally generated vector bundles with small |
title | Globally generated vector bundles with small |
title_full | Globally generated vector bundles with small |
title_fullStr | Globally generated vector bundles with small |
title_full_unstemmed | Globally generated vector bundles with small |
title_short | Globally generated vector bundles with small |
title_sort | globally generated vector bundles with small |
topic | Mathematical Physics and Mathematics |
url | http://cds.cern.ch/record/2635384 |
work_keys_str_mv | AT anghelcristian globallygeneratedvectorbundleswithsmall AT coandaiustin globallygeneratedvectorbundleswithsmall AT manolachenicolae globallygeneratedvectorbundleswithsmall |