Math 392C (Complex Geometry), Spring 2014

This is the main page for Math 392C (Complex Geometry), unique number 57175.


I am Andy Neitzke; my office is RLM 9.134. My office hours are 2-3:30pm on Wednesday, or by appointment.


This course meets TuTh from 9:30-11:00am, in RLM 12.166.


The main text will be Huybrechts, "Complex Geometry: An Introduction." Other useful resources are Griffiths and Harris, "Algebraic Geometry"; Voisin, "Hodge Theory and Complex Algebraic Geometry I"; Wells, "Differential Analysis on Complex Manifolds"; Moroianu, "Lectures on Kahler geometry."


I will assign exercises; I strongly encourage you to do them. I will mention a few exercises during lecture, but also will post slightly more organized exercise sheets (below.)


A very optimistic list of topics, along with some brief motivation, appears here. At most we can cover a couple of the more advanced ones. Therefore I would very much like feedback about which potential topics are of the most interest to you.

Here are some briefer comments. The first part of the course will be devoted to the basic technology of complex geometry. The main goals are the Hodge theory of Kahler manifolds and at least some of its consequences such as the Lefshetz theorems. Other phrases which will be explained along the way include "sheaf cohomology", "Dolbeault theorem", "holomorphic line bundle", and "divisor".

For the second part of the course we have somewhat more freedom, and what we do will depend somewhat on the tastes of the class. I hope to have time to explain the notion of variation of Hodge structure and the analogue of the Lefshetz theory for hyperkahler manifolds.

Lecture notes

I will post my notes from the lectures below. The mapping between files and lectures is not necessarily 1-1. Notes will be updated to correct errors/omissions where they are helpfully pointed out or where I notice them later. I apologize for whatever errors may remain.


The University of Texas at Austin provides upon request appropriate academic accommodations for qualified students with disabilities. For more information, contact the Office of the Dean of Students at 471-6259, 471-4641 TTY.