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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Degrees of high-dimensional subvarieties
of determinantal varieties

Author: B. A. Sethuraman
Journal: Proc. Amer. Math. Soc. 126 (1998), 9-14
MSC (1991): Primary 14M12
MathSciNet review: 1459148
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $n = p^ab$, where $p$ is a prime, and $\text{g.c.d. }(p,b)=1$. In $\mathbf{P}^{n^2-1}$, let $X_r$ be the variety defined by $\text{rank}\, ((x_{i,j})) \le n-r$. We show that any subvariety of $X_r$ of codimension less than $p^ar$ must have degree a multiple of $p$. We also show that the bounds on the codimension in our results are strict by exhibiting subvarieties of the appropriate codimension whose degrees are prime to $p$.

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Additional Information

B. A. Sethuraman
Affiliation: Department of Mathematics, California State University, Northridge, California 91330

Keywords: Determinantal varieties, degree
Received by editor(s): March 8, 1996
Additional Notes: Supported in part by an N.S.F. grant.
Communicated by: Ron Donagi
Article copyright: © Copyright 1998 American Mathematical Society