Introduction to Kaehler Geometry

2026/2027

Учебный год

ENG

Обучение ведется на английском языке

6

Кредиты

Кто читает:

Факультет математики

Статус:

Дисциплина общефакультетского пула

Когда читается:

3, 4 модуль

Преподаватель

Голота Алексей Сергеевич

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.