Resolutions of homogeneous bundles on ${\mathbb {P}}^2$

Giorgio Ottaviani; Elena Rubei

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Simona Faini (2006)

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In this work we will analyze the relation between the stability and the simplicity of a homogeneous vector bundle on a projective variety. Our main theorem shows that a homogeneous bundle is not destabilized by its homogeneous subbundles if and only if it is the tensor product of a stable homogeneous bundle and an irreducible representation. Then we give an example of a homogeneous bundle, which is simple, but not stable.

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Georges Elencwajg, O. Forster (1982)

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We study holomorphic vector bundles on non-algebraic compact manifolds, especially on tori. We exhibit phenomena which cannot occur in the algebraic case, e.g. the existence of 2-bundles that cannot be obtained as extensions of a sheaf of ideals by a line bundle. We prove some general theorems in deformations theory of bundles, which is our main tool.

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Displaying similar documents to “Resolutions of homogeneous bundles on ℙ 2 ”

Displaying similar documents to “Resolutions of homogeneous bundles on $ℙ^{2}$ ”