Grothendieck ring of varieties and birational geometry

Grothendieck ring of varieties and birational geometry

Semester
SoSe 2024

Lecturer
Pavel Sechin

Type of course (Veranstaltungsart)
Oberseminar

German title
Der Grothendieck Ring der algebraischen Varietäten

Contents
The goal of this seminar is to study some of the recent advances of applications of the Grothendieck ring of varieties to the questions of birational geometry.

In particular, we will address the properties of specialization of stable birationality and rationality in families with 'mild' singularities.

Literature

M. Larsen and V. Lunts. Motivic measures and stable birational geometry. Moscow Math. J., 2003.

J. Nicaise and E. Shinder. "The motivic nearby fiber and degeneration of stable rationality." Inventiones mathematicae, 2019.

M. Kontsevich and Y. Tschinkel. "Specialization of birational types." Inventiones mathematicae, 2019.

H.-Y. Lin and E. Shinder. "Motivic invariants of birational maps." Annals of Mathematics, 2024.

Time/Date
Fridays 15-17

Location
M 102

Course homepage
https://homepages.uni-regensburg.de/~sep03286/GrothendieckRing.html
(Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern)

Registration

Organisational meeting/distribution of topics: Email to pavel.sechin"at"ur.de
Registration for course work/examination/ECTS: FlexNow

Course work (Studienleistungen)

Presentation: Giving a seminar talk of roughly 90 minutes

Examination (Prüfungsleistungen)

Detailed written report of the seminar talk

Modules
MV, MSem

ECTS
4,5 ECTS