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Lagrangian subbundles and codimension 3 subcanonical subschemes
David Eisenbud, Sorin Popescu, and Charles Walter
Source: Duke Math. J. Volume 107, Number 3
(2001), 427-467.
Abstract
We show that a Gorenstein subcanonical codimension 3 subscheme Z⊂X=ℙN, N≥4, 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 quasi-projective 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 D. Buchsbaum and D. Eisenbud [6] and says that Z is Pfaffian.
We also prove codimension 1 symmetric and skew-symmetric analogues of our structure theorems.
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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1091737019
Mathematical Reviews number (MathSciNet): MR1828297
Digital Object Identifier: doi:10.1215/S0012-7094-01-10731-X
Zentralblatt MATH identifier: 01820806
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