By Alexandru Dimca
From the very starting, algebraic topology has built lower than the influ ence of the issues posed by means of attempting to comprehend the topological houses of complicated algebraic kinds (e.g., the pioneering paintings via Poincare and Lefschetz). particularly within the paintings of Lefschetz [Lf2], the assumption is made particular that singularities are very important within the learn of the topology even when it comes to delicate types. what's recognized these days concerning the topology of soft and singular vari eties is kind of striking. the various current effects should be approximately divided into periods as follows: (i) very common effects or theories, like stratified Morse thought and (mixed) Hodge thought, see, for example, Goresky-MacPherson [GM], Deligne [Del], and Steenbrink [S6]; and (ii) particular subject matters of significant subtlety and wonder, just like the learn of the funda psychological workforce of the supplement in [p>2 of a novel aircraft curve initiated by way of Zariski or Griffiths' thought touching on the rational differential varieties to the Hodge filtration at the center cohomology staff of a delicate projec tive hypersurface. the purpose of this booklet is strictly to introduce the reader to a few issues during this latter classification. many of the effects to be mentioned, in addition to the similar notions, are at the least 20 years outdated, and experts use them intensively and freely of their paintings. however, it's most unlikely to discover an enough intro duction to this topic, which provides an outstanding feeling for its family with different elements of algebraic geometry and topology.
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