Homogeneous projective varieties with degenerate secants
Author:
Hajime Kaji
Journal:
Trans. Amer. Math. Soc. 351 (1999), 533545
MSC (1991):
Primary 14M17, 14N05, 17B10, 20G05
MathSciNet review:
1621761
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Abstract: The secant variety of a projective variety in , denoted by , is defined to be the closure of the union of lines in passing through at least two points of , and the secant deficiency of is defined by . We list the homogeneous projective varieties with under the assumption that arise from irreducible representations of complex simple algebraic groups. It turns out that there is no homogeneous, nondegenerate, projective variety with and , and the variety is the only homogeneous projective variety with largest secant deficiency . This gives a negative answer to a problem posed by R. Lazarsfeld and A. Van de Ven if we restrict ourselves to homogeneous projective varieties.
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Additional Information
Hajime Kaji
Affiliation:
Department of Mathematics\ School of Science and Engineering\ Waseda University\ 341 Ohkubo\ Shinjukuku\ Tokyo 169, Japan
Email:
kaji@mse.waseda.ac.jp
DOI:
http://dx.doi.org/10.1090/S0002994799023788
PII:
S 00029947(99)023788
Received by editor(s):
April 9, 1996
Dedicated:
Dedicated to Professor Satoshi Arima on the occasion of his 70th birthday
Article copyright:
© Copyright 1999
American Mathematical Society
