×

On the real \(X\)-ranks of points of \(\mathbb P^n(\mathbb R)\) with respect to a real variety \(X \subset \mathbb P^n\). (English) Zbl 1209.14042

Summary: Let \(X \subset \mathbb P^n\) be an integral and non-degenerate \(m\)-dimensional variety defined over \(\mathbb R\). For any \(P \in \mathbb P^n(\mathbb R)\) the real \(X\)-rank \(r_{x,\mathbb R}(P)\) is the minimal cardinality of \(S \subset X(\mathbb R)\) such that \(P \in \langle S \rangle\). Here we extend to the real case an upper bound for the \(X\)-rank due to Landsberg and Teitler.

MSC:

14N05 Projective techniques in algebraic geometry
14H50 Plane and space curves
PDFBibTeX XMLCite
Full Text: DOI