Complex Geometry (Wintersemester 2024/25)
- Dozent*in: Jun.-Prof. Dr. Claudio Llosa Isenrich
- Veranstaltungen: Vorlesung (0100058), Übung (0100059)
- Semesterwochenstunden: 3+1
This lecture will give an introduction to complex geometry. Complex geometry is the study of smooth manifolds that are locally modelled on n-dimensional complex space and one of the main goals of complex geometry is to understand the topology of complex manifolds (usually) under some additional constraints. This is a classical topic that has its origins in problems like understanding the topology of smooth zero sets of polynomials in several variables in complex projective space.
After a short introduction to complex analysis in several variable, we will introduce the most important notions, such as complex manifolds, complex vector bundles and forms. We will then focus on the important class of compact Kähler manifolds, which includes the smooth zero sets of homogeneous polynomials in complex projective space and proceed to discuss the Hodge Decomposition Theorem for their cohomology. The latter is a fundamental result in complex geometry, which places strong constraints on the topology of compact Kähler manifolds.
| Termine | ||
|---|---|---|
| Vorlesung: | Donnerstag 11:30-13:00 (14-tägig) | Mathematikgebäude SR 2.059 |
| Freitag 8:00-9:30 | Mathematikgebäude SR 2.066 | |
| Übung: | Donnerstag 11:30-13:00 (14-tägig) | Mathematikgebäude SR 2.059 |
| Lehrende | ||
|---|---|---|
| Dozent | Jun.-Prof. Dr. Claudio Llosa Isenrich | |
| Sprechstunde: nach Vereinbarung | ||
| Zimmer 1.005 Kollegiengebäude Mathematik (20.30) | ||
| Email: claudio.llosa@kit.edu | Übungsleiter | Dr. Matteo Migliorini |
| Sprechstunde: nach Vereinbarung | ||
| Zimmer 1.015 Kollegiengebäude Mathematik (20.30) | ||
| Email: matteo.migliorini@kit.edu | ||