Art Waeterschoot

Beware that the documents below contain many mistakes and some are quite unfinished. So use with great care! Feel free to contact me with questions or remarks.

expository notes and slides:

slides for an expository talk on Berkovich curves, skeleta and weight functions for YRANT 2021
notes on Kähler norms and notes on Temkin's metrization of differential forms. For a study group (spring 2022) on this paper.
notes on Néron models (my master thesis, 2019)

slides on minimal model program (2023) for a study group on dual complexes of singularities (reworked from an earlier study group on degenerations of K3 varieties in 2021)
slides for a talk on Mazur's bounded torsion theorem for this study group (2020), following this course

Some more material from past study groups:

logarithmic geometry, hodge theory and degenerations (spring 2023)

We'll study logarithmic structures from scratch as well as two applications where they are used as a tool. One is steenbrink's algebraic construction of the limit mixed hodge structure, the second is log regular degenerations, see here for the outline and schedule.

april 11th (Nick): Introduction

april 18th (Art): log structures (notes)

apr 26th (Michael): log schemes (notes)

may 2nd (Ismaele): log smoothness (notes)

may 9th (Sasha): log analytic spaces

may 16th (Javier): hodge structures

may 23th (Irma): mixed hodge structures

may 30th (Art): limit MHS (notes)

June 6th (Nick): log regularity

June 13th (Art): log regular degenerations I

June 20th (Michael): log regular degenerations II

resolution of singularities (autumn 2021)

After studying some classical results we will work towards reading the following paper of Abramovich-Temkin-Wlodarczyk. A more detailed schedule with description of the contents can be found here.

oct 13th (Art): overview (slides)

oct 20th (Mathias): blowups and curves

oct 27th (Michael): surfaces and Jung's method (notes)

nov 3rd (Naud): resolution of toric varieties (notes)

nov 10th (Nick): local uniformisation of valuations (notes)

nov 17th (Floris): principalisation and maximal contact

nov 24th (Art): coefficient ideals and local invariant

dec 1st (Tim) : intro to stacks (notes)

dec 8th (Nick): weighted blowups and toric stacks (notes)

dec 15th (Tim): admissibility of centers (notes)

dec 22nd (Art): dream algorithm

unlikely intersections (autumn 2022): Following van den Dries and Masser-Zannier: website here