- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnlilne Submission ㆍMy Manuscript - For Reviewers - For Editors
 Dependent subsets of embedded projective varieties Bull. Korean Math. Soc. 2020 Vol. 57, No. 4, 865-872 https://doi.org/10.4134/BKMS.b190546Published online October 24, 2019Printed July 31, 2020 Edoardo Ballico University of Trento Abstract : 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. Keywords : Secant varietys $X$-ranks zero-dimensional schemes variety with only one ordinary double points OADP MSC numbers : 14N05 Supported by : The author was partially supported by MIUR and GNSAGA of INdAM (Italy) Downloads: Full-text PDF   Full-text HTML