×

Singularities and enriched cycles. (English) Zbl 1068.32021

This paper is concerned with local topological and geometric properties of a complex analytic space with arbitrary singularities, that is to say, with the variety defined by a complex analytic function \(f\) on an open subset of \(\mathbb C^n\). A goal is to produce algebraic data that provide useful information about Thom’s \(a_f\) condition and the Milnor fibrations. To this end, the author introduces a new concept, namely graded, enriched characteristic cycles, in order to encode Morse modules of strata with respect to a constructible complex of sheaves. This generalizes previous results on perverse sheaves.

MSC:

32S60 Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects)
32S30 Deformations of complex singularities; vanishing cycles
32S55 Milnor fibration; relations with knot theory
PDFBibTeX XMLCite
Full Text: DOI arXiv