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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The stability of exceptional bundles on complete intersection $3$-folds
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by Rosa Maria Miró-Roig and Helena Soares PDF
Proc. Amer. Math. Soc. 136 (2008), 3751-3757 Request permission

Abstract:

A very long-standing problem in Algebraic Geometry is to determine the stability of exceptional vector bundles on smooth projective varieties. In this paper we address this problem and we prove that any exceptional vector bundle on a smooth complete intersection $3$-fold $Y\subset \mathbb {P}^n$ of type $(d_1,\ldots ,d_{n-3})$ with $d_1+\cdots + d_{n-3}\leq n$ and $n\geq 4$ is stable.
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Additional Information
  • Rosa Maria Miró-Roig
  • Affiliation: Facultat de Matemátiques, Departament d’Àlgebra i Geometria, Universitat de Barcelona, Gran Via de les Corts Catalanes 585, 08007 Barcelona, Spain
  • MR Author ID: 125375
  • ORCID: 0000-0003-1375-6547
  • Email: miro@ub.edu
  • Helena Soares
  • Affiliation: ISCTE Business School, Departamento de Métodos Quantitativos, Edifício ISCTE, Av. Forças Armadas, 1649-026 Lisboa, Portugal
  • Email: helena.soares@ub.edu
  • Received by editor(s): January 29, 2007
  • Received by editor(s) in revised form: February 23, 2007
  • Published electronically: June 20, 2008
  • Additional Notes: The first author was partially supported by MTM2004-00666
    The second author was partially supported by Fundação para a Ciência e Tecnologia under grant SFRH/BD/16589/2004, and by Departamento de Métodos Quantitativos do Instituto Superior de Ciências do Trabalho e da Empresa
  • Communicated by: Ted Chinburg
  • © Copyright 2008 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 136 (2008), 3751-3757
  • MSC (2000): Primary 14F05
  • DOI: https://doi.org/10.1090/S0002-9939-08-09258-7
  • MathSciNet review: 2425712