2021 Advanced topics in Geometry H1

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Academic unit or major
Graduate major in Mathematics
Honda Nobuhiro 
Class Format
Media-enhanced courses
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Syllabus updated
Lecture notes updated
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Course description and aims

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.

Student learning outcomes

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

Competencies that will be developed

Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

regular lecture course

Course schedule/Required learning

  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

Out-of-Class Study Time (Preparation and Review)

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.


No textbook

Reference books, course materials, etc.

Barth, Hulek, Peters and van de Ven, "Compact complex surfaces", Springer
D. Huybrechts, "Lectures on K3 surfaces", Cambridge University Press

Assessment criteria and methods

based on homework assignments

Related courses

  • MTH.B202 : Introduction to Topology II
  • MTH.B301 : Geometry I
  • MTH.B302 : Geometry II

Prerequisites (i.e., required knowledge, skills, courses, etc.)

Assumed to have taken Advanced topics in Geometry G1 in 3Q.

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