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Let $X\subset \mathbb {P}^r$ be an integral and non-degenerate variety. Set $n:= \dim (X)$. Let $\rho (X)''$ be the maximal integer such that every zero-dimensional scheme $Z\subset X$ smoothable in $X$ is linearly independent. We prove that $X$ is linearly normal if $\rho (X)''\ge \lceil (r+2)/2\rceil$ and that $\rho (X)'' < 2\lceil (r+1)/(n+1)\rceil$, unless either $n=r$ or $X$ is a rational normal curve.
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참고문헌 (26)
참고문헌 신청
Bjorn Adlandsvik / 1987 / Joins and higher secant varieties. / MATHEMATICA SCANDINAVICA 61:213~222
A. Altman / 1970 / Introduction to Grothendieck Duality Theory / Springer-Verlag
E. Ballico / 2013 / Generalized Hamming weights of codes obtained from smooth plane curves / Afrika Matematika 24(4):565~569
Edoardo Ballico / 2012 / Decomposition of homogeneous polynomials with low rank / Mathematische Zeitschrift 271(3-4):1141~1149
E. Ballico / 2013 / Tensor ranks on tangent developable of Segre varieties / Linear and Multilinear Algebra 61(7):881~894
A. Altman / 1970 / Introduction to Grothendieck Duality Theory / Springer-Verlag
E. Ballico / 2013 / Generalized Hamming weights of codes obtained from smooth plane curves / Afrika Matematika 24(4):565~569
Edoardo Ballico / 2012 / Decomposition of homogeneous polynomials with low rank / Mathematische Zeitschrift 271(3-4):1141~1149
E. Ballico / 2013 / Tensor ranks on tangent developable of Segre varieties / Linear and Multilinear Algebra 61(7):881~894
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