Material covered

Homework: #1 #2

Lectures: TuTh 2–3:30 pm, Evans Hall Room 87
Course Control Number: 54952
Instructor: Constantin Teleman, 905 Evans, e-mail: teleman 'at' math
Office Hours: TuTh 11:30 am–1 pm, or by appointment.

Prerequisites: Math 214 and 215A.

Syllabus: The course will cover Riemann surfaces and higher-dimensional complex manifolds, with emphasis on the compact case.
Springer's book is a comprehensive treatment of Riemann surfaces (including a review of the topology of surfaces and covering spaces),
but we'll take a softer approach to that subject, covering the more elementary part of theory, including a discussion of elliptic curves;
see the Riemann Surface lecture notes linnked from my web page.
The difficult theorems will be done in the context of higher-dimensional manifolds. Wells' book (minus the appendix) is the basic reference here.
The key topics are complex manifolds, sheaves and Dolbeault cohomology, vector bundles, hermitian connections and their curvature,
elliptic regularity and the great theorems for compact Kähler manifolds: Hodge decomposition, Hard Lefschetz theorem,
the Kodaira vanishing theorem and (time-permitting) the embedding theorem.
We'll cover other topics if there is time.

Texts: George Springer, Introduction to Riemann Surfaces.
R.O. Wells, Differential Analysis on Complex Manifolds

Other Reading: Griffiths and Harris, Principles of Algebraic Geometry (more advanced topics)

Grading: There will be some homework assignments and some final paper suggestions – if you are enrolled in this course you should do one or the other.
Feel free to suggest paper topics yourself!