What question did this study set out to answer?

The research aims to establish lower bounds for the maximal number of A-singularities in algebraic surfaces.

March 4, 2026Comptes Rendus MathématiqueOpen Access

Some lower bounds for the maximal number of A -singularities in algebraic surfaces

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The research aims to establish lower bounds for the maximal number of A-singularities in algebraic surfaces.
Constructed algebraic surfaces using bivariate polynomials
Utilized previous works on nodal surfaces and Belyi polynomials
Derived explicit expressions involving classical Jacobi polynomials
Demonstrated the construction of surfaces with a significantly high number of A-singularities
Provided new explicit expressions for certain polynomial families

Implication

Constructs algebraic surfaces with many A-singularities, suggesting new possibilities in singularity theory.

Abstract

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.

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Cite This Study

Juan García Escudero (2026) studied this question.

synapsesocial.com/papers/69a7cce8d48f933b5eed8bbe https://doi.org/10.5802/crmath.815

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Implication

Constructs algebraic surfaces with many A-singularities, suggesting new possibilities in singularity theory.

Some lower bounds for the maximal number of A -singularities in algebraic surfaces

Key Points

Implication

Abstract

Discussion

Cite This Study

Some lower bounds for the maximal number of A -singularities in algebraic surfaces

Key Points

Implication

Abstract

Discussion

Cite This Study

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