Tsinghua University Shiing-Shen Chern Distinguished Lecture | |
Student No.： | 100 |
Time： | 16:30-17:30, 2017.10.18/ 10.20/ 10.23/ 10.25 |
Instructor： | Claire Voisin |
Place： | Lecture Hall, Floor 3, Jinchun Yuan West Building |
Starting Date： | 2017-10-18 |
Ending Date： | 2017-10-25 |
Lecture 1 Introductory lecture on Kähler and Calabi-Yau geometry
I will describe the complex differential geometric viewpoint on Calabi-Yau geometry, and some consequences.
Lecture 2 Hodge theory: applications to deformation theory and topology
Hyper-Kähler manifolds are easy to deform and their deformations are almost entirely controled by their period points (work of Beauville, Huybrechts and Verbitsky). I will also explain how the existence of the Beauville-Bogomolov form follows from the local study of the period map.
Lecture 3 Constructing hyper-Kähler manifolds from algebraic geometry
The simplest hyper-Kähler manifolds are K3 surfaces and there are many other types that have been constructed starting from K3 surfaces. More surprisingly, cubic fourfolds also led to the construction of several families, with the advantage over K3 that they have 20 parameters, while algebraic K3 surfaces have only 19 parameters.
Lecture 4 Deformation types of hyper-Kähler manifolds via degeneration.
I will explain a simple but useful generalization of Huybrechts' theorem on birational versus deformation equivalence, and apply it to several classes of examples.