Identifying variable points on a smooth curve.
Infinitesimal deformations of complex surfaces with boundary.
Infinitesimal deformations of quotient surface singularities
Integral closure of modules and Whitney equisingularity.
Irregular fibers of complex polynomials in two variables.
For a complex polynomial in two variables we study the morphism induced in homology by the embedding of an irregular fiber in a regular neighborhood of it. We give necessary and sufficient conditions for this morphism to be injective, surjective. Particularly this morphism is an isomorphism if and only if the corresponding irregular value is regular at infinity. We apply these results to the study of vanishing and invariant cycles.