Mathematical Sciences Research Institute

Home » Workshop » Schedules » Resolution in characteristic 0 using weighted blowing up

Resolution in characteristic 0 using weighted blowing up

Recent Progress in Moduli Theory May 06, 2019 - May 10, 2019

May 07, 2019 (09:30 AM PDT - 10:30 AM PDT)
Speaker(s): Dan Abramovich (Brown University)
Location: MSRI: Simons Auditorium
  • Resolution of singularities

  • Algebraic stacks

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification



This is joint work with Michael Tëmkin (Jerusalem) and Jarosław Włodarczyk (Purdue), a side product of our work on functorial semistable reduction. A similar result was discovered by G. Marzo and M. McQuillan. Given a variety $X$, one wants to blow up the worst singular locus, show that it gets better, and iterate until the singularities are resolved. Examples such as the whitney umbrella show that this iterative process cannot be done by blowing up smooth loci – it goes into a loop. We show that there is a functorial way to resolve varieties using weighted blowings up, in the stack-theoretic sense. To an embedded variety $X \subset Y$ one functorially assigns an invariant $(a_1,\ldots,a_k)$, and a center locally of the form $(x_1^{a_1} , \ldots , x_k^{a_k})$, whose stack-theoretic weighted blowing up has strictly smaller invariant under the lexicographic order.

Asset no preview Notes 643 KB application/pdf Download
Video/Audio Files


H.264 Video 869_26587_7728_5-Abramovich.mp4
Troubles with video?

Please report video problems to itsupport@msri.org.

See more of our Streaming videos on our main VMath Videos page.