Algebraic Geometry II

Instructor: Harry Tamvakis

Lectures: Tuesday and Thursday 12:30 - 1:45, Math 0104

Office: Math 4419
Office hours: By appointment
Telephone: (301)-405-5120

Course guide:

Main text: D. Huybrechts, "Complex Geometry: An Introduction", Springer-Verlag, 2005.

This course continues the study of Riemann surfaces and complex algebraic geometry from Math 606, as taught last semester. In Math 607, we will focus more on spaces of dimension greater than one. We will discuss the basic theory of analytic spaces and study theta functions, the theta divisor, and prove Riemann's theorem about meromorphic functions and theta. We will then discuss Grassmannians, flag manifolds, and construct characteristic classes of complex vector bundles, from the point of view of hermitian differential geometry. The ultimate goal of the course is to understand how the Riemann-Roch theorem generalizes to higher dimensions, namely, the Hirzebruch-Riemann-Roch and Grothendieck-Riemann-Roch theorems.

I plan to distribute some homework problems during the course.

Other useful book references:

- R. Narasimhan, "Compact Riemann Surfaces", Birkhauser, 1996.

- Griffiths and Harris, "Principles of Algebraic Geometry", Wiley-Interscience, 1994.

- R. O. Wells, "Differential Analysis on Complex Manifolds", 3rd edition, Springer-Verlag, 2008.