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arXiv · 2105.10345

Some variational properties of tangent directions at infinity of real algebraic sets

Si Tiep Dinh·Tien Son Pham
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Abstract

In this paper, we relate the set of asymptotic critical values of a polynomial function $f$ with the set of discontinuity of two functions, the multivalued function which associate to each value $t$ the set of tangent directions at infinity of the fiber $f^{-1}(t)$ and the composition of the $(n-2)$-dimensional volume function with the first one. This gives necessary conditions of equisingularity at infinity for the family of the fibers of a real polynomial function.

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Si Tiep Dinh, Tien Son Pham. 2021-05-21. Some variational properties of tangent directions at infinity of real algebraic sets. https://arxiv.org/abs/2105.10345

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