An example of indecomposable vector bundle of rank $n-1$ on $P^n$

Algebraic vector bundles on projective spaces: A problem list

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methods

Holomorphic vector bundles on ℙn

Moduli reflexiver Garben und Flächen von kleinem Grad in ℙ 4

We describe a technique which permits a uniform construction of a number of low rank bundles, both known and new. In characteristic two, we obtain rank two bundles on P 5 . In characteristic p, we obtain rank two bundles on P 4 and rank three bundles on P 5 . In arbitrary characteristic, we obtain rank three bundles on P 4 and rank two bundles on the quadric S 5 in P 6 .

Construction of low rank vector bundles on ⁴ and ⁵

One classifies the globally generated vector bundles on with the first Chern class c1 = 3. The case c1 = 1 is very easy, the case c1 = 2 was done in [42], the case c1 = 3, rank =2 was settled in [21] and the case c1 ≤ 5, rank = 2 in [10]. Our work is based on Serre's theorem relating vector bundles of rank = 2 with codimension 2 lci subschemes and its generalization for higher ranks, considered firstly by Vogelaar in [48].

Globally generated vector bundles on Pn with c1=3

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An example of indecomposable vector bundle of rank $n-1$ on $P^n$

Citations

Algebraic vector bundles on projective spaces: A problem list

Holomorphic vector bundles on ℙn

Moduli reflexiver Garben und Flächen von kleinem Grad in ℙ 4

Construction of low rank vector bundles on ⁴ and ⁵

Globally generated vector bundles on Pn with c1=3

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