Titlebook: Handbook of Geometry and Topology of Singularities II; José Luis Cisneros-Molina,Dũng Tráng Lê,José Seade Book 2021 Springer Nature Switze

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Algebro-Geometric Equisingularity of Zariski,arity Theory. In the first part of this survey, we consider Zariski equisingular families of complex analytic or algebraic hypersurfaces. We also discuss how to construct Zariski equisingular deformations. In the second part, we present Zariski equisingularity of hypersurfaces along a nonsingular su

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Intersection Homology,tion between cycles, are no longer true for a singular variety. A huge and fantastic step forward was taken by Mark Goresky and Robert MacPherson by the simple but brilliant idea of rediscovering duality by restricting oneself to chains only meeting the singular part of a stratified singular variety

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,Milnor’s Fibration Theorem for Real and Complex Singularities,r critical points. In this chapter we revisit the classical theory and we glance at some areas of current research. We start with a glimpse at the origin of the fibration theorem, which is motivated by the study of exotic spheres. We then discuss an elementary example where all the ingredients of th

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,Lê Cycles and Numbers of Hypersurface Singularities,of the hypersurface, it is effectively algebraically calculable, it determines the homotopy-type of the Milnor fiber, and its constancy in a family implies that Thom’s . condition is satisfied and that the ambient topological-type of the hypersurface is constant (outside of possibly one dimension).

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Introduction to Mixed Hypersurface Singularity,nt of algebraic geometry, it is more convenient to study the tubular fibration . where . with . and . [., .]. After this fundamental result, many researches have been carried out in various related directions. Among them, the generalization of the fibration structure and related geometry to the situ