Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Typical and Admissible ranks over fields   Let $X(\RR)$ be a geometrically connected variety defined over $\RR$ and such
that the set of all its (also complex) points $X(\CC)$ is non-degenerate.
  We introduce the notion of \emph{admissible rank} of a point $P$ with respect
to $X$ to be the minimal cardinality of a set of points of $X(\CC)$ such that
$P\in \langle S \rangle$ that is stable under conjugation.
  Any set evincing the admissible rank can be equipped with a \emph{label}
keeping track of the number of its complex and real points. We show that in the
case of generic identifiability there is an open dense euclidean subset of
points with certain admissible rank for any possible label. Moreover we show
that if $X$ is a rational normal curve than there always exists a label for the
generic element. We present two examples in which either the label doesn't
exists or the admissible rank is strictly bigger than the usual complex rank.

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The categories of this paper are: cond-mat
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The categories of this paper are: physics
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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: dg-ga