A Vector Bundle of Rank 2 on P1 x P3

H. Lange

A Vector Bundle of Rank 2 on P1 x P3

alg-geom 2015-06-30 v1 Algebraic Geometry

Authors: H. Lange

Abstract

The paper studies a rank 2 vector bundle on P1 x P3. Similarly to the Horrocks - Mumford bundle on P4 this vector bundle encodes a lot of geometric information. It is defined via the Serre construction by an abelian surface in P1 x P3. The bundle is stable with respect to O(1,1), its jumping lines are determined. Morover it is shown that it is closely related to a double structue on P1 x P1 embedded in P1 x P3 as well as to a certain pencil of quadrics of degree 4 in P3.

Keywords

vector bundles P1 x P3 Horrocks-Mumford bundle abelian surface jumping lines

Cite

@article{arxiv.alg-geom/9506021,
  title  = {A Vector Bundle of Rank 2 on P1 x P3},
  author = {H. Lange},
  journal= {arXiv preprint arXiv:alg-geom/9506021},
  year   = {2015}
}

Comments

20 pages, LaTeX

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