Splitting criteria for vector bundles on singular quadrics
نویسندگان
چکیده
منابع مشابه
A Few Splitting Criteria for Vector Bundles
We prove a few splitting criteria for vector bundles on a quadric hypersurface and Grassmannians. We give also some cohomological splitting conditions for rank 2 bundles on multiprojective spaces. The tools are monads and a Beilinson’s type spectral sequence generalized by Costa and Miró-Roig.
متن کاملSplitting Criteria for Vector Bundles on Higher Dimensional Varieties
We generalize Horrocks’ criterion for the splitting of vector bundles on projective space. We establish an analogous splitting criterion for vector bundles on a class of smooth complex projective varieties of dimension ≥ 4, over which every extension of line bundles splits.
متن کاملMonads and Vector Bundles on Quadrics
We improve Ottaviani’s splitting criterion for vector bundles on a quadric hypersurface and obtain the equivalent of the result by Rao, Mohan Kumar and Peterson. Then we give the classification of rank 2 bundles without ”inner” cohomology on Qn (n > 3). It surprisingly exactly agrees with the classification by Ancona, Peternell and Wisniewski of rank 2 Fano bundles. Introduction A monad on P or...
متن کاملMonads and Rank Three Vector Bundles on Quadrics
In this paper we give the classification of rank 3 vector bundles without ”inner” cohomology on a quadric hypersurface Qn (n > 3) by studying the associated monads. Introduction A monad on P or, more generally, on a projective variety X, is a complex of three vector bundles 0 → A α −→ B β −→ C → 0 such that α is injective as a map of vector bundles and β is surjective. Monads have been studied ...
متن کاملA Splitting Criterion for Vector Bundles on Higher Dimensional Varieties
We generalize Horrocks’ criterion for the splitting of vector bundles on projective space. We establish an analogous splitting criterion for vector bundles on arbitrary smooth complex projective varieties of dimension ≥ 4, which asserts that a vector bundle E on X splits iff its restriction E|Y to an ample smooth codimension 1 subvariety Y ⊂ X splits.
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ژورنال
عنوان ژورنال: International Journal of Contemporary Mathematical Sciences
سال: 2007
ISSN: 1314-7544
DOI: 10.12988/ijcms.2007.07162