Schur quadrics, cubic surfaces and rank 2 vector bundles over the projective plane

Details Schur quadrics, cubic surfaces and rank 2 vector bundles over the projective plane Schur quadrics, cubic surfaces and rank 2 vector bundles over the projective plane

1993-04-13

arxiv.org/abs/alg-geom/9304005v1

Mathematics

Algebraic Geometry

27 pages, plain TEX

Scientific paper

A cubic surface in $P^3$ is known to contain 27 lines, out of which one can form 36 Schlafli double - sixes i.e., collections $l_1,...,l_6, l'_1,..., l'_6\}$ of 12 lines such that each $l_i$ meets only $l'_j, j\neq i$ and does not meet $l_j, j\neq i$. In 1881 F. Schur proved that any double - six gives rise to a certain quadric $Q$ , called Schur quadric which is characterized as follows: for any $i$ the lines $l_i$ and $l'_i$ are orthogonal with respect to (the quadratic form defining) $Q$. The aim of the paper is to relate Schur's construction to the theory of vector bundles on $P^2$ and to generalize this construction along the lines of the said theory.

Affiliated with

Also associated with

No associations

Rating

Schur quadrics, cubic surfaces and rank 2 vector bundles over the projective plane 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 Schur quadrics, cubic surfaces and rank 2 vector bundles over the projective plane, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Schur quadrics, cubic surfaces and rank 2 vector bundles over the projective plane will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-581444