By Alexandru Dimca
From the very starting, algebraic topology has built less than the influ ence of the issues posed through attempting to comprehend the topological homes of complicated algebraic kinds (e.g., the pioneering paintings by way of Poincare and Lefschetz). in particular within the paintings of Lefschetz [Lf2], the assumption is made particular that singularities are vital within the research of the topology even with regards to delicate forms. what's recognized these days concerning the topology of gentle and singular vari eties is kind of striking. the numerous present effects could be approximately divided into sessions as follows: (i) very normal effects or theories, like stratified Morse idea and (mixed) Hodge concept, see, for example, Goresky-MacPherson [GM], Deligne [Del], and Steenbrink [S6]; and (ii) particular subject matters of serious subtlety and sweetness, just like the learn of the funda psychological team of the supplement in [p>2 of a unique airplane curve initiated by way of Zariski or Griffiths' thought bearing on the rational differential varieties to the Hodge filtration at the center cohomology crew of a soft projec tive hypersurface. the purpose of this booklet is strictly to introduce the reader to a couple issues during this latter type. lots of the effects to be mentioned, in addition to the similar notions, are a minimum of twenty years previous, and experts use them intensively and freely of their paintings. however, it truly is most unlikely to discover an enough intro duction to this topic, which supplies an outstanding feeling for its kinfolk with different elements of algebraic geometry and topology.
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