Geometry and Moduli Space of Certain Rank-4 Vector Bundles on ${\mathbb P}^4$

Details Geometry and Moduli Space of Certain Rank-4 Vector Bundles on ${\mathbb P}^4$ Geometry and Moduli Space of Certain Rank-4 Vector Bundles on ${\mathbb P}^4$

2000-11-20

arxiv.org/abs/math/0011147v1

Mathematics

Algebraic Geometry

54 pages, Latex

Scientific paper

Mathematical instanton bundles of rank 4 and $c_2=2$ on ${\mathbb P}^4$ have a smoothquasiprojective moduli space, which is shown via a direct GIT construction. A complete classification of jumping lines of these vector bundles is obtained. The duals of these bundles are described. Dimension computations and irreducibility proofs for some "interesting" subsets of the moduli space are presented. Restrictions of vector bundles from ${\mathbb P}^4$ to ${\mathbb P}^3$ are shown to produce mathematical instanton bundles on ${\mathbb P}^3$.

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