Resumen de Algebraic Morse theory and the weak factorization theorem

Jaroslaw Wlodarczyk

• 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.