À¶Ý®ÊÓƵ

Cynthia Dai, University of À¶Ý®ÊÓƵ

Resolution of Singularities via Stacky Blow-ups

We follow Dan Abramovich and Ming Hao Quek’s paper on resolution of singularity by multi-weighted blowups. This line of work is first motivated to give a more natural and motivated proof of Hironaka’s result, and that leads to the notion of weighted blowup, where you repeatedly blowing up the worst singular locus via weighted blowups. The problem with this is at the end you do not get an ambient space that’s smooth DM, but log smooth(specifically it’s toroidal DM stack). Using the technique of multi-weighted blowup introduced by Satriano, we can improve this result to get a logarithmic resolution of singularity with a smooth ambient space.

MC 5403