## General information

This the webpage of the seminar on deformation theory to be held during winter semester 2020/2021 at University of Amsterdam.

Intuitively, we will be interested in infinitesimal changes of algebraic varieties and various structures on them such as subschemes, line bundles and sheaves. This might considered as local analysis of appropriate moduli spaces, e.g., Hilbert scheme, Picard schemes, moduli of varieties.

We will meet according to the following schedule:
Date: Every Wednesday at 11:00($+\varepsilon$)
Location: Korteweg-de Vries Institute for Mathematics, room F3.20
Online: On Zoom [Meeting ID: 978 3804 1835 Password: 396626]

## Programme of the seminar:

Here comes a more specific programme of the seminar. Click for more details on the talk contents and some supplementary references.

1. [Wed, 16.09.2020] Introduction to deformation theory (Maciek Zdanowicz)
2. [Wed, 23.09.2020] Structures over dual numbers (Wouter Rienks) [Recording and Wouter's notes]
3. [Wed, 30.09.2020] Infinitesimal lifting property and deformations of smooth varieties (Dirk van Bree) [Recording and Dirk's notes]
4. [Wed, 07.10.2020] Functors of Artin rings and formal moduli (Renjie Lyu) [Renjie's notes]
5. [Thu, 15.10.2020, 10:00] Schlessinger prorepresentability and hull existence criteria (Mike Daas) [Recording of Mike's talk]
6. [Wed, 21.10.2020] Tangent and obstruction theories (Kees Kok) [Recording and Kees' notes]
7. [Wed, 28.10.2020] Exal category and naive cotangent complex (Emelie Arvidsson) [Emmi's notes]
8. [Wed, 4.11.2020] Cotangent complex and its deformation theoretic applications (Maciej Zdanowicz) [Recording and Maciek's notes]
9. [Wed, 11.11.2020] Construction of the cotangent complex (Lenny Taelman) [Recording and Lenny's notes]
10. [Wed, 18.11.2020] Schlessinger-Lichtenbaum complex and deformations of singularities (Olivier de Gaay Fortman) [Recording and Olivier's notes]
11. [Wed, 25.11.2020] Murphy laws on moduli spaces (Simon Pepin Lehalleur) [Recording of Simon's talk]
12. [Wed, 2.12.2020] Bogomolov-Tian-Todorov theorem (Emma Brakkee) [Recording and Emma's notes]
13. [Wed, 9.12.2020] Overview of singularities of Hilbert schemes of points (Sergej Monavari) [Recording and Sergej's notes]
14. [Wed, 16.12.2020] Lifting from characteristic $p$ to characteristic zero (Jack Davies) [Recording and Jack's notes]
15. [Wed, 06.01.2021] On the birational nature of lifting (Przemysław Grabowski) [Recording and Przemek's notes]
16. [Wed, 13.01.2021] Bend and break & Mori's resolution of Hartshorne's conjecture (Diletta Martinelli) [Meeting ID: 978 3804 1835 Password: 396626]

## References

In the talks we will likely follow some of the following references.

We will also discuss some of the following papers:

• C. Liedtke, M. Satriano - On the birational nature of lifting
• R. Vakil - Murphy’s law in algebraic geometry: Badly-behaved deformation spaces
• J. Jelisiejew - Pathologies on the Hilbert scheme of points

## Organizers:

The seminar is run by Lenny Taelman and Maciek Zdanowicz
All inquiries should be directed to m.e.zdanowicz [at] uva [dot] nl

## COVID-19 regulations

• There can be at most 10 people in the seminar room (1 speaker and 9 audience members). At all times keep 1.5m distance.
• If you come to the seminar, you must also book a desk at the institute.
• Every talk can be followed from home using zoom (and you can ask questions from home). Also the speaker can choose to give the talk from home
• If you have any of the symptoms (cold, fever, sore throat, loss of smell or taste, ...) then stay home (and get tested)

The ventilation of the seminar room has been tested, and based on that we are allowed to be 10 people in the room. However: because of the ventilation it may get chilly in the room, so bring a sweater. If more than 10 people want to come to the seminar, we will set up a rotation schedule.