MA 725 — Fall 2023
Introduction to complex geometry

Instructor

Name: Maciej Szczesny
Office: CDS 431
Office hours: Mon. 10:30-11:30, Fri. 12-2
E-mail: szczesny at math.bu.edu

Course info

Lectures:
TTh 11-12:15, PSY B50

Text

Complex Geometry - D. Huybrechts, Springer

About the course: The subject of MA 725 this fall will be complex geometry, which can be viewed as differential geometry in the category of complex manifolds. Although the methods are complex analytic, the subject is in some ways closer in spirit to algebraic geometry than smooth geometry, and plays a central role in modern theoretical physics. We will cover:

complex manifolds and their local/global structure
Kahler manifolds and basic Hodge theory
Holomorphic vector bundles and sheaf cohomology
applications of cohomology such as the HRR and the Kodaira embedding/vanishing theorems
(time permitting) deformations of complex structures via DGLAs

Useful References:

Robert Lazarsfeld's notes Complex geometry
Christian Snell's notes Complex manifolds

Evaluation: Based on bi-weekly problem sets

Homework Problems

MA 725 — Fall 2023 Introduction to complex geometry

MA 725 — Fall 2023
Introduction to complex geometry