On the real \(X\)-ranks of points of \(\mathbb{P}^n(\mathbb{R})\) with respect to a real variety \(X\subset\mathbb{P}^n\)

Edoardo Ballico

Abstract


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.

Keywords


Ranks; real variety; structured rank

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References


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DOI: http://dx.doi.org/10.17951/a.2010.54.2.15-19
Data publikacji: 2016-07-29 10:39:54
Data złożenia artykułu: 2016-07-28 18:46:17

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