Schwarzenberger Bundles of Arbitrary Rank on the Projective Space
نویسنده
چکیده
We introduce a generalized notion of Schwarzenberger bundle on the projective space. Associated to this more general definition, we give an ad-hoc notion of jumping subspaces of a Steiner bundle on P (which in rank n coincides with the notion of unstable hyperplane introduced by Vallès, Ancona and Ottaviani). For the set of jumping hyperplanes, we find a sharp bound for its dimension. We also classify those Steiner bundles whose set of jumping hyperplanes have maximal dimension and prove that they are generalized Schwarzenberger bundles.
منابع مشابه
1 1 Ju n 20 03 Holomorphic rank - 2 vector bundles on non - Kähler elliptic surfaces
The existence problem for vector bundles on a smooth compact complex surface consists in determining which topological complex vector bundles admit holomorphic structures. For projective surfaces, Schwarzenberger proved that a topological complex vector bundle admits a holomorphic (algebraic) structure if and only if its first Chern class belongs to the Neron-Severi group of the surface. In con...
متن کامل. A G ] 1 1 Ju n 20 03 Holomorphic rank - 2 vector bundles on non - Kähler elliptic surfaces
The existence problem for vector bundles on a smooth compact complex surface consists in determining which topological complex vector bundles admit holomorphic structures. For projective surfaces, Schwarzenberger proved that a topological complex vector bundle admits a holomorphic (algebraic) structure if and only if its first Chern class belongs to the Neron-Severi group of the surface. In con...
متن کاملProjective Models of the Twistor Spaces of Joyce Metrics
We provide a simple algebraic construction of the twistor spaces of arbitrary Joyce’s self-dual metrics on the 4-manifold H 2 × T 2 that extend smoothly to nCP, the connected sum of complex projective planes. Indeed, we explicitly realize projective models of the twistor spaces of arbitrary Joyce metrics on nCP in a CP-bundle over CP, and show that they contain the twistor spaces of H 2 × T 2 a...
متن کاملVector Bundles on Fano 3-folds without Intermediate Cohomology
A well-known result of Horrocks (see [Ho]) states that a vector bundle on a projective space has not intermediate cohomology if and only if it decomposes as a direct sum of line bundles. There are two possible generalizations of this result to arbitrary varieties. The first one consists of giving a cohomological characterization of direct sums of line bundles. This has been done for quadrics an...
متن کاملVector Bundles on Products of Varieties with n-blocks Collections
Here we consider the product of varieties with n-blocks collections . We give some cohomological splitting conditions for rank 2 bundles. A cohomological characterization for vector bundles is also provided. The tools are Beilinson’s type spectral sequences generalized by Costa and Miró-Roig. Moreover we introduce a notion of CastelnuovoMumford regularity on a product of finitely many projectiv...
متن کامل