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15 April 2001 Lagrangian subbundles and codimension 3 subcanonical subschemes
David Eisenbud, Sorin Popescu, Charles Walter
Duke Math. J. 107(3): 427-467 (15 April 2001). DOI: 10.1215/S0012-7094-01-10731-X

Abstract

We show that a Gorenstein subcanonical codimension 3 subscheme ZX=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.

Citation

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David Eisenbud. Sorin Popescu. Charles Walter. "Lagrangian subbundles and codimension 3 subcanonical subschemes." Duke Math. J. 107 (3) 427 - 467, 15 April 2001. https://doi.org/10.1215/S0012-7094-01-10731-X

Information

Published: 15 April 2001
First available in Project Euclid: 5 August 2004

zbMATH: 1069.14053
MathSciNet: MR1828297
Digital Object Identifier: 10.1215/S0012-7094-01-10731-X

Subjects:
Primary: 14M07
Secondary: 13D02, 14J60, 14M12

Rights: Copyright © 2001 Duke University Press

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Vol.107 • No. 3 • 15 April 2001
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