Theory of K3 surfaces are treated. K3 surfaces are compact simply connected Kaehler surface with vanishing Ricci curvature,
and play significant role in complex geometry. This course succeeds Advanced topics in Geometry G1 in 3Q.
To understand that a large part of the theory of K3 surfaces are dominated by second cohomology groups.
K3 surface, Kummer surface, K3 lattice, Hodge isometry, Torelli theorem, Kaehler cone, period map, period domain, polarized K3 surface, Weyl group, nodal class
|✔ Specialist skills||Intercultural skills||Communication skills||Critical thinking skills||Practical and/or problem-solving skills|
regular lecture course
|Course schedule||Required learning|
|Class 1||Definition and fundamental properties of K3 surfaces, examples||Definitions and properties|
|Class 2||Kummer surfaces||Definitions and properties|
|Class 3||Torelli theorem on K3 surfaces||Definitions and properties|
|Class 4||moduli space of marked K3 surfaces, 1||Definitions and properties|
|Class 5||moduli space of marked K3 surfaces, 2||Definitions and properties|
|Class 6||local Torelli theorem||Definitions and properties|
|Class 7||polarized K3 surfaces and period domain||Definitions and properties|
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Barth, Hulek, Peters and van de Ven, "Compact complex surfaces", Springer
D. Huybrechts, "Lectures on K3 surfaces", Cambridge University Press
based on homework assignments
Assumed to have taken Advanced topics in Geometry G1 in 3Q.