Fibrés vectoriels de rang deux sur $¶^2$ provenant d'un revêtement double

Details Fibrés vectoriels de rang deux sur $¶^2$ provenant d'un revêtement double Fibrés vectoriels de rang deux sur $¶^2$ provenant d'un revêtement double

2008-06-20

arxiv.org/abs/0806.3355v2

Mathematics

Algebraic Geometry

quinze pages

Scientific paper

Since Schwarzenberger and his celebrated paper called "Vector bundles on the projective plane" we know that any rank two vector bundle on $\P^2$ is a direct image of a line bundle on a double covering of the plane. This theorem suggests to study the rank two vector bundles according to the branch curve of the covering which they come from. Thus, in the first part we prove that, given a double covering ramified over an irreducible curve $C_{2r}$ with degree $2r$, the jumping lines of fixed order (order depending on $r$ and on the parity of the rank two vector bundle) of the direct images vector bundles are necessarely $r$-tangent to $C_{2r}$. In the second part we concentrate on the case $r=2$. Then we give a list of vector bundles for which the jumping lines are exactly the bitangent lines to the branch quartic.

Affiliated with

Also associated with

No associations

Rating

Fibrés vectoriels de rang deux sur $¶^2$ provenant d'un revêtement double does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Fibrés vectoriels de rang deux sur $¶^2$ provenant d'un revêtement double, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Fibrés vectoriels de rang deux sur $¶^2$ provenant d'un revêtement double will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-371183