2023/2024
Функции многих комплексных переменных
Статус:
Дисциплина общефакультетского пула
Кто читает:
Факультет математики
Когда читается:
3, 4 модуль
Охват аудитории:
для всех кампусов НИУ ВШЭ
Язык:
английский
Кредиты:
6
Контактные часы:
72
Course Syllabus
Abstract
Analysis of several complex variables is not studied in the usual university program. At the same time it is a necessary pre-requisite to study many important domains of contemporary mathematics such as algebraic geometry, complex dynamics, singularity theory, differential equations etc. While holomorphic functions of several complex variables share many basic properties of functions of one variable, new phenomena of analytic extention occurs. For example, they can have neither isolated singularities, nor compact sets of singularities. Each complex space of dimension at least two contains a proper domain that is biholomorphically equivalent to the ambient space (Fatou——Bieberbach domain). Theory of holomorphic convexity and Stein manifolds together with basic sheave theory allow to prove important extension and approximation theorems. The GAGA principle in algebraic geometry says that every analytic object on a complex projective algebraic manifold is algebraic. The cours will cover the above mentioned topics, including basic analytic set theory, biholomorphic automorphisms and introduction to complex dynamics.