Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Newton polygons and families of polynomials   We consider a continuous family $(f_s)$, $s\in[0,1]$ of complex polynomials
in two variables with isolated singularities, that are Newton non-degenerate.
We suppose that the Euler characteristic of a generic fiber is constant (or
equivalently the sum of the affine Milnor number and the Milnor number at
infinity $\mu(s)+\lambda(s)$ is constant). We firstly prove that the set of
critical values at infinity depends continuously on $s$, and secondly that the
degree of the $f_s$ is constant (up to an algebraic automorphism of $\Cc^2$).

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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
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The categories of this paper are: cs
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc