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The research aims to explore irreducible germs of generic morphisms to understand the singularities of their branch curves.

On irreducible germs of generic morphisms

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The research aims to explore irreducible germs of generic morphisms to understand the singularities of their branch curves.
Examined the set of irreducible germs $f_P$ associated with generic morphisms $f: S \to \mathbb P^2$.
Analyzed branch curve germs $B_P \subset V_p$ with singularities characterized by coprime integers $k_1$ and $k_2$.
Utilized the concept of equisingular deformation equivalence to draw conclusions about these singularities.
Identified that the singularities of the branch curves relate to those defined by $x^{k_1}-y^{k_2}=0$ with coprime $k_1$ and $k_2$.
Established a framework for understanding the deformation equivalence between different singularities in projective geometry.

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We examine irreducible germs of generic morphisms with equisingular branch curves, highlighting their significance.

Victor Stepanovich Kulikov (2026) studied this question.

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