Abstract:
In this series of talks, we will present the proof of functorial resolution of singularities (in terms of smooth morphisms and equivalent marked ideals) following the approach of Bierstone and Milman. The series of talks are intended to be elementary, but some previous knowledge on algebraic geometry or complex analysis would be beneficial. We present a resolution of singularities of marked ideals, and we briefly discuss the necessary adaptations to a variety or analytic space. We will focus on the invariant introduced by Bierstone and Milman (which we present via an inductive construction) and on the notion of test sequences (in comparison with weak test sequences). If we have time, we will briefly discuss the differences between the presented algorithm with other resolution of singularities algorithms. El curso constará de tres sesiones: lunes 20, martes 21 y miércoles 22 de febrero de 17:00 a 18:00.