Room P3.10, Mathematics Building

Orlando Villamayor, Universidad Autonoma de Madrid
On constructive resolution of singularities

There are two central theorems in algebraic geometry due to Hironaka: resolution of singularities, and Log-principalization of ideals. The second theorem relates to the elimination of base points of a linear system, and hence to the study of morphisms among smooth projective varieties. We intend to give some indications of an alternative simplified proof of both theorems, which has lead to various computer implementations in recent years.