Steiner Bundles on the Hyperquadric Q_n ⊂ ℙⁿ⁺¹, n ≥ 3

Abstract

We study Steiner bundles on the smooth hyperquadric Q_n ⊂ ℙⁿ⁺¹, for n ≥ 3. These are vector bundles E defined by an exact sequence of the form

We characterize generic exceptional and generic simple Steiner bundles and we prove that generic exceptional Steiner bundles are stable.

Key Words:

• Exceptionality
• Stability
• Vector bundles

2000 Mathematics Subject Classification:

• 14J60

ACKNOWLEDGMENTS

I would like to thank Rosa Maria Miró-Roig and Laura Costa for their uncountable support, suggestions, and encouragement.

Partial financial support by Fundação para a Ciência e Tecnologia under grant SFRH/BD/16589/2004, and Departamento de Métodos Quantitativos do Instituto Superior de Ciências do Trabalho e da Empresa.

Notes

Communicated by R. Piene.