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Forum Mathematicum

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Volume 29, Issue 3


Exceptional bundles of homological dimension ${k}$

Rosa María Miró-Roig
  • Facultat de Matemàtiques, Departament d’Àlgebra i Geometria, Universitat de Barcelona, Gran Via de les Corts Catalanes 585, 08007 Barcelona, Spain
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/ Helena SoaresORCID iD: http://orcid.org/0000-0002-6472-0061
Published Online: 2016-07-12 | DOI: https://doi.org/10.1515/forum-2015-0058


We characterize exceptional vector bundles on n of arbitrary homological dimension defined by a linear resolution. Moreover, we determine all Betti numbers of such resolution.

Keywords: Exceptional bundles; homological dimension; Steiner bundles

MSC 2010: 14J10; 14J60


  • [1]

    Bohnhorst G. and Spindler H., The stability of certain vector bundles on n, Complex Algebraic Varieties (Bayreuth 1990), Lecture Notes in Math. 1507, Springer, Berlin (1992), 39–50. Google Scholar

  • [2]

    Brambilla M. C., Simplicity of vector bundles on Pn and exceptional vector bundles and exceptional bundles Ph.D. thesis, University of Florence, Florence, 2004. Google Scholar

  • [3]

    Brambilla M. C., Cokernel bundles and Fibonacci bundles, Math. Nachr. 281 (2008), no. 4, 499–516. Google Scholar

  • [4]

    Dolgachev I. and Kapranov M., Arrangements of hyperplanes and vector bundles on n, Duke Math. J. 71 (1993), no. 3, 633–664. Google Scholar

  • [5]

    Drézet J.-M. and Le Potier J., Fibrés stables et fibrés exceptionnels sur 2, Ann. Sci. Éc. Norm. Supér. (4) 18 (1985), no. 2, 193–243. Google Scholar

  • [6]

    Ellia P. and Hirschowitz A., Voie ouest. I. Génération de certains fibrés sur les espaces projectifs et application, J. Algebraic Geom. 1 (1992), no. 4, 531–547. Google Scholar

  • [7]

    Gorodentsev A. L. and Kuleshov S. A., Helix theory, Mosc. Math. J. 4 (2004), no. 2, 377–440. Google Scholar

  • [8]

    Grayson D. R. and Stillman M. E., Macaulay2, a software system for research in algebraic geometry, available at www.math.uiuc.edu/Macaulay2/.

  • [9]

    Marchesi S. and Prata D., Simplicity and exceptionality of syzygy bundles over n, Ann. Mat. Pura Appl. (4) 195 (2016), no. 1, 41–58. Google Scholar

  • [10]

    Miró-Roig R. M., Determinantal Ideals, Progr. Math. 264, Birkhäuser, Basel, 2008. Google Scholar

  • [11]

    Okonek C., Schneider M. and Spindler H., Vector bundles on complex projective spaces, Progr. Math. 3, Birkhäuser, Boston, 1980. Google Scholar

  • [12]

    Soares H., Steiner vector bundles on algebraic varieties, Ph.D. thesis, University of Barcelona, Barcelona, 2008. Google Scholar

About the article

Received: 2015-03-30

Revised: 2016-03-01

Published Online: 2016-07-12

Published in Print: 2017-05-01

Funding Source: Fundação para a Ciência e a Tecnologia

Award identifier / Grant number: PTDC/MAT-GEO/0675/2012

Funding Source: Ministerio de Economía y Competitividad

Award identifier / Grant number: MTM2013-45075-P

Funding Source: Fundação para a Ciência e a Tecnologia

Award identifier / Grant number: SFRH/BSAB/105740/2014

Both authors were partially supported by project PTDC/MAT-GEO/0675/2012, Fundação para a Ciência e Tecnologia. The first author also received partial support from project MTM2013-45075-P, Ministerio de Economia y Competitividad. The second author was partially supported by the sabbatical grant SFRH/BSAB/105740/2014, Fundação para a Ciência e Tecnologia, and acknowledges the funding and hospitality from the Departament d’Àlgebra i Geometria of Universitat de Barcelona, where part of the work of this paper was developed.

Citation Information: Forum Mathematicum, Volume 29, Issue 3, Pages 701–715, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2015-0058.

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