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.
The Probabilistic Method in Real Singularity Theory / Lerario, Antonio; Stecconi, Michele. - In: ARNOLD MATHEMATICAL JOURNAL. - ISSN 2199-6792. - (2024), pp. 1-16. [10.1007/s40598-023-00240-7]
The Probabilistic Method in Real Singularity Theory
Lerario, Antonio;Stecconi, Michele
2024-01-01
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.File in questo prodotto:
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