Comptes Rendus
Article de recherche - Géométrie algébrique
Some lower bounds for the maximal number of $A$-singularities in algebraic surfaces
[Quelques bornes inférieures pour le nombre maximal de singularités de type $A$ dans les surfaces algébriques]
Juan García Escudero1 orcid
1Madrid, Spain
Comptes Rendus. Mathématique, Volume 364 (2026), pp. 59-69

We construct algebraic surfaces with a large number of type $A$ singularities. Bivariate polynomials presented in previous works for the construction of nodal surfaces and certain families of Belyi polynomials are used. In some cases explicit expressions in terms of classical Jacobi polynomials are obtained.

Nous construisons des surfaces algébriques comportant un grand nombre de singularités de type $A$. Nous utilisons les polynômes à deux variables présentés dans des travaux antérieurs pour la construction de surfaces nodales et certaines familles de polynômes de Belyi. Dans certains cas, nous obtenons des expressions explicites en termes de polynômes de Jacobi classiques.

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Révisé le :
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DOI : 10.5802/crmath.815
Classification : 14B05, 14J17, 14J70
Keywords: Singularities, algebraic surfaces
Mots-clés : Singularités, surfaces algébriques

Juan García Escudero  1

1 Madrid, Spain
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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Juan García Escudero. Some lower bounds for the maximal number of $A$-singularities in algebraic surfaces. Comptes Rendus. Mathématique, Volume 364 (2026), pp. 59-69. doi: 10.5802/crmath.815

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