NT & AG Seminar "A dream desingularization algorithm", Michael Temkin

Mon, 27/05/201914:30-15:30
Abstract: Any birational geometer would agree that the best algorithm for resolution of singularities should run by defining a simple invariant of the singularity and iteratively blowing up its maximality locus. The only problem is that already the famous example of Whitney umbrella shows that this is impossible, and all methods following Hironaka had to use some history and resulted in more complicated algorithms. Nevertheless, in a recent work with Abramovich and Wlodarczyk we did construct such an algorithm, and an independent description of a similar algorithm was done by McQuillan and Marzo. The novelty is in enlarging the pool of admissible blow ups: we allow weighted blow ups of smooth centers, and working with orbifolds we achieve that the ambient space nevertheless remains smooth. In this talk I will explain some ideas of the old and new algorithms and describe simple examples, including the Whitney umbrella, in the old and new algorithms.