Decomposition of simple singularities of functions

Singular hypersurfaces possessing infinitely many star points

“…Lemma 4.4 implies that for L fixed, there exist polynomials L 2 and L 3 such that the singularities of X on the line Λ are all of the type A k and satisfy formula (⋆). From [6,7], it follows that such singularities are the least worse that can deform into d − 1 singularities of type A d−1 , hence the generic statement follows.…”

A Few Problems on Monodromy and Discriminants

“…The so-called Lyashko-Looijenga covering (see [6], [15]) is a strong tool for constructing (or proving the existence of) the perturbations of simple singularities with prescribed topological properties, such as singularity types of different critical points, or intersection matrices of vanishing cycles, see e.g. [8]. The real version of this tool allows one to construct and enumerate all topologically different Morsifications of real simple singularities, see [7], [4], [18].…”

О Топологии Волновых Фронтов В Пространствах Небольших Размерностей

“…c ⃝ В. Д. Седых, 2012 ребер возврата и гладких ветвей) и A 3 1 (трансверсальные пересечения трех гладких ветвей). Ростки соответствующих поверхностей представлены на рис.…”