Lectures: Tuesday and Thursday 12:30 - 1:45, MTH 0102
Office: Math 4419
Office hours: By appointment
Main text: D. Huybrechts, "Complex Geometry: An Introduction",
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",
- R. O. Wells, "Differential Analysis on Complex Manifolds",
3rd edition, Springer-Verlag, 2008.