The Probabilistic Method in Real Singularity Theory

Lerario, Antonio; STECCONI, Michele

doi:10.1007/s40598-023-00240-7

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The Probabilistic Method in Real Singularity Theory

Lerario, Antonio; STECCONI, Michele

2024 • In Arnold Mathematical Journal, 10 (3), p. 355 - 370

Peer reviewed

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https://hdl.handle.net/10993/66872

DOI
10.1007/s40598-023-00240-7

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Keywords :

Random polynomials; Real algebraic geometry; Singularity theory; Mathematics (all)

Abstract :

[en] 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.

Disciplines :

Mathematics

Author, co-author :

Lerario, Antonio ; Scuola Internazionale Superiore di Studi Avanzati, Trieste, Italy

STECCONI, Michele ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)

External co-authors :

yes

Language :

English

Title :

The Probabilistic Method in Real Singularity Theory

Publication date :

September 2024

Journal title :

Arnold Mathematical Journal

ISSN :

2199-6792

eISSN :

2199-6806

Publisher :

Springer Science and Business Media Deutschland GmbH

Volume :

Issue :

Pages :

355 - 370

Peer reviewed :

Peer reviewed

Additional URL :

https://link.springer.com/content/pdf/10.1007/s40598-023-00240-7.pdf

Funders :

Scuola Internazionale Superiore di Studi Avanzati - SISSA

Funding text :

The authors wish to thank R. Piene and B. Shapiro for interesting discussions and for bringing the problem to their attention. A. Lerario is supported by the Knuth and Alice Wallenberg Foundation. M. Stecconi was supported by the Luxembourg National Research Fund (Grant: 021/16236290/HDSA).Open access funding provided by Scuola Internazionale Superiore di Studi Avanzati - SISSA within the CRUI-CARE Agreement.

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Bibliography

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