Complements of discriminants of real singularities of type X₁₀

2023/01/17 by Vassiliev, Victor A.
#14Q30 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2301.06994

Abstract

A conjecturally complete list of connected components of complements of discriminant varieties (aka wave fronts) of smooth function singularities of type X₁₀³ and X₁₀¹ is presented; it are the first examples of not semi-quasihomogeneous plane function singularities. It is shown that the complements of discriminants of singularities of classes X₉^± and X₁₀¹ have non-trivial 1-dimensional homology groups, in contrast to all simple singularity classes.

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