Research Seminar: Resolution of singularities

We will study the new results by Abramovich, Temkin and Włodarczyk on resolution of singularities over a field $k$ of characteristic $0$. Their work, combined with a “destackification theorem” by Bergh gives a new proof of Hironaka’s celebrated theorem. If one is willing to “stay in the world of stacks”, one obtains resolution with additional nice features (functoriality, and the resolution is given by a straight-forward process where one defines an invariant at each point which says “how singular” the point is, and at each step the maximum of the invariant drops after a suitable “stacky weighted blow-up”.

Program: pdf (updated Oct. 10)

Date Title Speaker
17.10.2019 Introduction Ulrich Görtz
24.10.2019 Reminder on blow-ups and examples Chirantan Chowdhury
31.10.2019 Weighted blow-ups Pavel Sechin
07.11.2019 Resolution for toric varieties Louis-Clément Lefèvre
14.11.2019 Resolution for toric stacks Xiaoyu Zhang
21.11.2019 The Zariski-Riemann space Andrea Marrama
28.11.2019 Coefficient ideals and maximal contact Vytautas Paškūnas
05.12.2019 Definition of the invariant Heer Zhao
12.12.2019 Admissibility Lukas Pottmeyer
19.12.2019 Proof of the main theorem Jochen Heinloth
09.01.2020 The destackification theorem I Daniel Greb
16.01.2020 The coarse space of a stack Xuchen Zhang
23.01.2020 The destackification theorem II Jan Kohlhaase
30.01.2020 Program discussion for next term