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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...

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Detalles Bibliográficos
Autores principales: Anghel, Cristian, Coandă, Iustin, Manolache, Nicolae
Lenguaje:eng
Publicado: American Mathematical Society 2018
Materias:
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.
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institution Organización Europea para la Investigación Nuclear
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publishDate 2018
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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