Algebraic Morse theory and the weak factorization theorem

• Autores: Jaroslaw Wlodarczyk
• Localización: Proceedings oh the International Congress of Mathematicians: Madrid, August 22-30,2006 : invited lectures / coord. por Marta Sanz Solé , Javier Soria de Diego , Juan Luis Varona Malumbres , Joan Verdera , Vol. 2, 2006, ISBN 978-3-03719-022-7, págs. 653-682
• Idioma: inglés
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• Resumen

  • We develop a Morse-like theory for complex algebraic varieties. In this theory a Morse function is replaced by a C.-action. The critical points of the Morse function correspond to connected fixed point components. ¡°Passing through the fixed points¡± induces some simple birational transformations called blow-ups, blow-downs and flips which are analogous to spherical modifications.

    In classical Morse theory by means of a Morse function we can decompose the manifold into elementary pieces . ¡°handles¡±. In algebraic Morse theory we decompose a birational map between two smooth complex algebraic varieties into a sequence of blow-ups and blow-downs with smooth centers.