Details

Edoardo Ballico^[a]

The \(b\)-secant variety of a smooth curve has a codimension \(1\) locally closed subset whose points have rank at least \(b + 1\)

Pages: 345-351
Received: 23 June 2017
Accepted in revised form: 27 September 2017
Mathematics Subject Classification (2010): 14N05, 14H50.
Keywords: Secant variety, \(X\)-rank, tangential variety, join of two varieties, tangentially degenerate curve, strange curve
Author address:
[a]: Department of Mathematics, University of Trento, 38123 Povo (TN), Italy

Abstract: Take a smooth, connected and non-degenerate projective curve \(X\subset \mathbb{P}^r\), \(r\ge 2b+2\ge 6\), defined over an algebraically closed field with characteristic \(0\) and let \(\sigma _b(X)\) be the \(b\)-secant variety of \(X\). We prove that the \(X\)-rank of \(q\) is at least \(b+1\) for a non-empty codimension \(1\) locally closed subset of \(\sigma _b(X)\).

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