## 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.## References

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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