Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ideal theory and classification of isoparametric hypersurfaces   The classification of isoparametric hypersurfaces with four principal
curvatures in the sphere interplays in a deep fashion with commutative algebra,
whose abstract and comprehensive nature might obscure a differential geometer's
insight into the classification problem that encompasses a wide spectrum of
geometry and topology. In this paper, we make an effort to bridge the gap by
walking through the important part of commutative algebra central to the
classification of such hypersurfaces, such that all the essential
ideal-theoretic ingredients are laid out in a way as much intuitive, motivating
and geometric with rigor maintained as possible. We then explain how we
developed the technical side of the entailed ideal theory, pertinent to
isoparametric hypersurfaces with four principal curvatures, for the
classification done in our papers~\cite{CCJ},~\cite{Ch1} and~\cite{Ch3}.

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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex