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Description: |
(joint work with Rosa Maria Miró-Roig)
Steiner bundles on projective spaces were first defined by Dolgachev and
Kapranov as vector bundles E on P^n fitting in an exact sequence of the form
0 --> /O/(-1)^s --> /O/^t --> E --> 0.
Steiner bundles have rank t-s>= n and it is well known that when
equality holds Steiner bundles are stable and, in
particular, simple. More recently, M. C. Brambilla studied
Steiner bundles on a complex projective space P^n, for n>= 3. She
characterised general Steiner bundles and gave a complete
description of simple and non-simple general Steiner bundles. Moreover,
she proved that any exceptional Steiner
bundle on P^n is stable, for all n>=2.
We generalise the notion of Steiner bundle by defining and studying a
new family of vector bundles on smooth irreducible algebraic varieties.
We call them /Steiner bundles of type/ (F_0,F_1).
We characterise exceptional and simple general Steiner bundles of type
(F_0,F_1) and we also
study the stability of some exceptional Steiner bundles of type (F_0,F_1).
Furthermore, we give a cohomological characterisation of these bundles.
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