V. Vassiliev

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math.AG2025

Complements of discriminants of real parabolic function singularities. II

V. A. Vassiliev

We list all connected components of sets of non-discriminant functions near all {\em parabolic} function singularities (which are the second most important family of singularity cl…

math.AG2025

Complements of caustics of the real $J_{10}$ singularities

V. A. Vassiliev

The complete list of connected components of the set of Morse functions in the deformations of function singularities of class $J_{10}$ is given. Thus, the isotopy classification o…

math.AG2023

Isotopy classification of Morse polynomials of degree 4 in $R^{2}$

V. A. Vassiliev

We introduce a system of invariants of isotopy classes of Morse polynomials $R^{2} \to R^{1}$ , prove its completeness for polynomials of degrees $\leq 4$ , calculate…

Complements of discriminants of real parabolic function singularities. II

Complements of caustics of the real J10​ singularities

Isotopy classification of Morse polynomials of degree 4 in R2

Complements of caustics of the real $J_{10}$ singularities

Isotopy classification of Morse polynomials of degree 4 in $R^{2}$