Homogeneous projective varieties with degenerate secants |
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| Authors: | Hajime Kaji |
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| Affiliation: | Department of Mathematics, School of Science and Engineering, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo 169, Japan |
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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, non-degenerate, 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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| Keywords: | |
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