By Alexandru Dimca
From the very starting, algebraic topology has built lower than the influ ence of the issues posed via attempting to comprehend the topological homes of complicated algebraic forms (e.g., the pioneering paintings by means of Poincare and Lefschetz). specially 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 soft forms. what's recognized these days in regards to the topology of delicate and singular vari eties is kind of remarkable. the various latest effects should be approximately divided into sessions as follows: (i) very normal effects or theories, like stratified Morse conception and (mixed) Hodge idea, see, for example, Goresky-MacPherson [GM], Deligne [Del], and Steenbrink [S6]; and (ii) particular issues of significant subtlety and wonder, just like the learn of the funda psychological team of the supplement in [p>2 of a unique aircraft curve initiated through Zariski or Griffiths' conception touching on the rational differential types to the Hodge filtration at the heart cohomology staff of a gentle projec tive hypersurface. the purpose of this e-book 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 lots of the effects to be mentioned, in addition to the similar notions, are at the very least 20 years outdated, and experts use them intensively and freely of their paintings.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 supplies a great feeling for its family with different elements of algebraic geometry and topology.
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