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arXiv · 2308.00050

The probabilistic method in real singularity theory

Antonio Lerario·Michele Stecconi
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Abstract

We explain how to use the probabilistic method to prove the existence of real polynomial singularities with rich topology, i.e. with total Betti number of the maximal possible order. We show how similar ideas can be used to produce real algebraic projective hypersurfaces with a rich structure of umbilical points.

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Antonio Lerario, Michele Stecconi. 2023-07-31. The probabilistic method in real singularity theory. https://arxiv.org/abs/2308.00050

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