Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Strict inclusions of high rank loci   For a given projective variety $X$, the high rank loci are the closures of
the sets of points whose $X$-rank is higher than the generic one. We show
examples of strict inclusion between two consecutive high rank loci. Our first
example is for the Veronese surface of plane quartics. Although Piene had
already shown an example when $X$ is a curve, we construct infinitely many
curves in $\mathbb P^4$ for which such strict inclusion appears. For space
curves, we give two criteria to check whether the locus of points of maximal
rank 3 is finite (possibly empty).

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The categories of this paper are: q-bio
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The categories of this paper are: econ
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys