2026/2027

Introduction to Kaehler Geometry

Type: Optional course (faculty)

Delivered by: Faculty of Mathematics

Where: Faculty of Mathematics

When: 3, 4 module

Open to: students of all HSE University campuses

Instructors: Alexey Golota

Language: English

ECTS credits: 6

Contact hours: 72

Course Syllabus

Abstract

Compact Kaehler manifolds form a class of compact complex manifolds that is remarkable from the complex-analytic, differential-geometric and algebro-geometric viewpoints. This class includes smooth complex projective varieties, as well as many non-algebraic complex manifolds. The main advantage of compact Kaehler manifolds is the existence of the so-called Hodge decomposition on cohomology. Building the theory of compact Kaehler manifolds and proving the existence of Hodge decomposition requires methods from a few important areas of modern mathematics (complex analysis, differential geometry, algebraic geometry, functional analysis and PDEs). This course will be a concise introduction to geometry of compact Kaehler manifolds.