Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Puiseux expansions and non-isolated points in algebraic varieties   We consider the problem of deciding whether a common solution to a
multivariate polynomial equation system is isolated or not. We present
conditions on a given truncated Puiseux series vector centered at the point
ensuring that it is not isolated. In addition, in the case that the set of all
common solutions of the system has dimension 1, we obtain further conditions
specifying to what extent the given vector of truncated Puiseux series
coincides with the initial part of a parametrization of a curve of solutions
passing through the point.

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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
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The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
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The categories of this paper are: econ
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The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: physics
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: nlin