1. Description

The basic object of study in algebraic geometry are algebraic varieties, which are defined by vanishing of systems of polynomial equations. As part of the structure of a variety, one remembers not only the topological spaces defined by these vanishing loci but also the algebras that give rise to them. Nevertheless, one may wonder to what extent the topological space alone determines the variety. Such determination fails in low dimension but, surprisingly, holds in sufficiently high dimension, according to recent results of Kollár (that build on earlier work of Lieblich and Olsson). The goal of this series of lectures is to explain these results.

Some background reading would be good in order to make sure that the audience is familiar with the basic notions about varieties and algebraic geometry. Chapter I of Mumford's red book would be a good starting point and should be very accessible. Afterwards one could read Chapters 2-4 of Liu's book for further background. Both of these texts have exercises that the students can try, I will also try to insert exercises in my lectures.

Online via google meet: https://meet.google.com/ccm-puqs-uch

Main reference:

• J. Kollar, What determines a variety? arXiv:2002.12424v2

2. Speaker

• Kestutis Cesnavicius (CNRS, Université Paris-Sud).

3. Tentative schedule and venue

Schedule:
9h30 - 11h30 Thursday – Oct. 1, 8, 22, 29.
14h-16h Wednesday – Oct. 14.

Venue: Room 302 A5 Institute of Mathematics -VAST.

4. Registration

By sending an email to Doan Trung Cuong ( This email address is being protected from spambots. You need JavaScript enabled to view it. ) with some information:

• Your full name.
• Name and address of your university/institute.
• Your position (undergraduate/master/PhD students, lecturer, professor, …).
• Your contact: email address and telephone number.