A Vector Bundle of Rank 2 on P1 x P3

Details A Vector Bundle of Rank 2 on P1 x P3 A Vector Bundle of Rank 2 on P1 x P3

1995-06-26

arxiv.org/abs/alg-geom/9506021v1

Mathematics

Algebraic Geometry

20 pages, LaTeX

Scientific paper

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.

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