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Lefschetz Fibrations and real Lefschetz fibrations

Nermin Salepci (2014)

Winter Braids Lecture Notes

This note is based on the lectures that I have given during the winter school Winter Braids IV, School on algebraic and topological aspects of braid groups held in Dijon on 10 - 13 February 2014. The aim of series of three lectures was to give an overview of geometrical and topological properties of 4-dimensional Lefschetz fibrations. Meanwhile, I could briefly introduce real Lefschetz fibrations, fibrations which have certain symmetry, and could present some interesting features of them.This note...

Local approximation of semialgebraic sets

Massimo Ferrarotti, Elisabetta Fortuna, Les Wilson (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Let A be a closed semialgebraic subset of euclidean space of codimension at least one, and containing the origin O as a non-isolated point. We prove that, for every real s 1 , there exists an algebraic set V which approximates A to order s at O . The special case s = 1 generalizes the result of the authors that every semialgebraic cone of codimension at least one is the tangent cone of an algebraic set.

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