Fundamental groups of compact Kähler manifolds (Sommersemester 2025)
- Dozent*in: Jun.-Prof. Dr. Claudio Llosa Isenrich,
- Veranstaltungen: Seminar (0120750)
- Semesterwochenstunden: 2
Premeeting: Tuesday 18.02.2024, 14:00-15:00 Uhr, Room: SR 2.058
Seminar dates: Presumably as Blockseminar either in the first week of the term break (04.08. - 08.08.) or in the Pentecost break (10.06. - 13.06.). This will be confirmed soon.
Language: Talks in English are encouraged, but German talks are allowed
Prerequisites: Knowledge of a first course in Complex Geometry and of fundamental groups will be assumed.
Registration: To register or if you have any questions, please write to claudio.llosa@kit.edu, before the premeeting.
| Termine | ||
|---|---|---|
| Seminar: | ||
| Lehrende | ||
|---|---|---|
| Seminarleitung | Jun.-Prof. Dr. Claudio Llosa Isenrich | |
| Sprechstunde: nach Vereinbarung | ||
| Zimmer 1.005 Kollegiengebäude Mathematik (20.30) | ||
| Email: claudio.llosa@kit.edu | Seminarleitung | Dr. Matteo Migliorini |
| Sprechstunde: nach Vereinbarung | ||
| Zimmer 1.015 Kollegiengebäude Mathematik (20.30) | ||
| Email: matteo.migliorini@kit.edu | ||
A classical problem in Algebraic Geometry, dating back to the early 20th century, is the study of the topology of smooth complex projective varieties, that is, compact complex submanifolds of the complex projective space. One of the most important topological invariants is the fundamental group. This motivates the study of fundamental groups of smooth complex projective varieties, an active field, which has its origins in works of Serre in the 1950s.
It is an open problem, known as the Kodaira problem, if every fundamental group of a compact Kähler manifold (short: Kähler groups) is also a fundamental group of a smooth complex projective variety. It is thus customary to study the potentially larger class of Kähler groups, which is what we will do in this seminar. This is a topic at the intersection of many areas of mathematics. Following an introduction of basic notions, examples and constraints, we will focus on connections between algebra and geometry. In particular, we will explore constraints coming from morphisms from Kähler groups onto fundamental groups of closed hyperbolic surfaces, and we will see that such morphisms are induced by holomorphic maps on the underlying compact Kähler manifolds.
Literaturhinweise
To get an idea of the possible topics you may consult the following literature. More precise information on topics of talks and corresponding literature will be provided to participants before the premeeting. Some individual talks may require further literature that will be provided by us.
- J. Amoros, M. Burger, K. Corlette, D. Kotschick, D. Toledo, Fundamental Groups of Compact Kähler Manifolds, Math. Surveys Monogr., 44, AMS, 1996.
- P. Py, Lectures on Kähler groups, to appear in Princeton University Press, 2025.