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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



The connectedness of symmetric and skew-symmetric degeneracy loci: even ranks

Author: Loring W. Tu
Journal: Trans. Amer. Math. Soc. 313 (1989), 381-392
MSC: Primary 14M12; Secondary 14C99
MathSciNet review: 930069
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Abstract: A degeneracy locus is the set of points where a vector-bundle map has rank at most a given integer. Such a set is symmetric or skew-symmetric according as whether the vector-bundle map is symmetric or skew-symmetric. We prove a connectedness result, first conjectured by Fulton and Lazarsfeld, for skew-symmetric degeneracy loci and for symmetric degeneracy loci of even ranks.

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Keywords: Connectedness, determinantal varieties, degeneracy loci, symmetric degeneracy loci, skew-symmetric degeneracy loci, ample vector bundles, isotropic subspaces, rank
Article copyright: © Copyright 1989 American Mathematical Society