Proceedings of the American Mathematical Society

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



The stability of exceptional bundles on complete intersection $ 3$-folds

Authors: Rosa Maria Miró-Roig and Helena Soares
Journal: Proc. Amer. Math. Soc. 136 (2008), 3751-3757
MSC (2000): Primary 14F05
Published electronically: June 20, 2008
MathSciNet review: 2425712
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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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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

Helena Soares
Affiliation: ISCTE Business School, Departamento de Métodos Quantitativos, Edifício ISCTE, Av. Forças Armadas, 1649-026 Lisboa, Portugal

Keywords: Exceptional vector bundles, stability
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
Article copyright: © Copyright 2008 American Mathematical Society