Arrondo Esteban, Enrique
(2010)
*Schwarzenberger bundles of arbitrary rank on the projective space.*
Journal of the london mathematical society-second series, 82
(Part 3).
pp. 697-716.
ISSN 0024-6107

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Official URL: http://jlms.oxfordjournals.org/content/82/3/697.full.pdf+html

## Abstract

We introduce a generalized notion of Schwarzenberger bundle on the projective space. Associated to this more general definition, we give an ad hoc notion of jumping subspaces of a Steiner bundle on P(n) (which in rank n coincides with the notion of unstable hyperplane introduced by Valles, Ancona and Ottaviani). For the set of jumping hyperplanes, we find a sharp bound for its dimension. We also classify those Steiner bundles whose set of jumping hyperplanes have maximal dimension and prove that they are generalized Schwarzenberger bundles.

Item Type: | Article |
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Uncontrolled Keywords: | Vector-bundles; Hyperplanes; Curves |

Subjects: | Sciences > Mathematics > Algebraic geometry |

ID Code: | 14753 |

References: | 1. V. Ancona and G. Ottaviani, ‘Unstable hyperplanes for Steiner bundles and multidimensional matrices’, Adv. Geom. 1 (2001) 165–192. 2. A. Beauville, ‘Vector bundles and theta functions on curves of genus 2 and 3’, Amer. J. Math. 128 (2006) 607–618. 3. I. Dolgachev and M. Kapranov, ‘Arrangements of hyperplanes and vector bundles on Pn’, Duke Math. J. 71 (1993) 633–664. 4. J. Harris, Algebraic geometry: a first course (Springer, Berlin, 1992). 5. R. Re, ‘Multiplication of sections and Clifford bounds for stable vector bundles on curves’, Comm. Algebra 26 (1998) 1931–1944. 6. R. L. E. Schwarzenberger, ‘Vector bundles on the projective plane’, Proc. London Math. Soc. 11 (1961) 623–640. 7. J. C. Sierra, ‘A degree bound for globally generated vector bundles’, Math. Z. 262 (2009) 517–525. 8. H. Soares, ‘Steiner vector bundles on algebraic varieties’, PhD Thesis, Barcelona, 2008. 9. J. Vall`es, ‘Nombre maximal d’hyperplans instables pour un fibr´e de Steiner’, Math. Z. 233 (2000) 507–514. 10. J. Vall`es, ‘Fibr´es de Schwarzenberger et fibr´es logarithmiques g´en´eralis´es’, Preprint, 2008, Math. Z., arXiv:0810.1603v2 [math.AG], http://www.springerlink.com/content/417321652k337643/fulltext.pdf. |

Deposited On: | 17 Apr 2012 11:26 |

Last Modified: | 06 Feb 2014 10:08 |

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