Lagrangian Subbundles and Codimension 3 Subcanonical Subscheme

Details Lagrangian Subbundles and Codimension 3 Subcanonical Subscheme Lagrangian Subbundles and Codimension 3 Subcanonical Subscheme

1999-06-25

arxiv.org/abs/math/9906170v2

Mathematics

Algebraic Geometry

AMS-LaTeX, diagrams.sty, 35 pages, minor revisions

Scientific paper

We show that a Gorenstein subcanonical codimension 3 subscheme Z in X = P^N, N > 3, can be realized as the locus along which two Lagrangian subbundles of a twisted orthogonal bundle meet degenerately, and conversely. We extend this result to singular Z and all quasiprojective ambient schemes X under the necessary hypothesis that $Z$ is strongly subcanonical in a sense defined below. A central point is that a pair of Lagrangian subbundles can be transformed locally into an alternating map. In the local case our structure theorem reduces to that of Buchsbaum-Eisenbud and says that Z is Pfaffian. We also prove codimension one symmetric and skew-symmetric analogues of our structure theorems.

Affiliated with

Also associated with

No associations

Rating

Lagrangian Subbundles and Codimension 3 Subcanonical Subscheme 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 Lagrangian Subbundles and Codimension 3 Subcanonical Subscheme, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Lagrangian Subbundles and Codimension 3 Subcanonical Subscheme will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-507958