This is the main page for **Math 392C (Complex Geometry)**, unique number **56530**.

I am Andy Neitzke; my office is RLM 9.134. My office hours are on Thursday and Friday from 11am-12 noon.

This course meets MWF from 3-4pm, in RLM 10.176.

The main text will be **Huybrechts, "Complex Geometry: An Introduction."** Other useful
resources are 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.) My plan was to post one each Saturday; this was a little too optimistic.

If you need a grade for the course, you should either turn in (at least) 1 problem from each exercise sheet, or write a short essay about some topic in complex geometry that interests you. I can suggest topics on request. The due date for these assignments is May 11.

- 01: Exercises
- 02: Exercises
- 03: Exercises
- 04: Exercises
- 05: Exercises
- 06: Exercises
- 07: Exercises
- 08: Exercises (from Huybrechts)

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.

A more detailed and very optimistic list of topics, along with some brief motivation,
appears here. It seems clear that 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.

I have removed the lecture notes as of March 2014; they contained too many errors.

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.