** **
Math 555

## Complex Manifolds II, Spring 2014

**Time**: MWF 12:00-12:50

**Location**: 305 Taft Hall

**Instructo**r: Henri Gillet

**Office:** 405 SEO

**Phone: ** 413-2157

**Email: ** gillet@uic.edu

**Course Website:**
http://www.math.uic.edu/~henri/math313.html

**Office Hours: ** Monday 2:00-3:00, and Wednesday
3:00-4:00 or by request.

**Course Description**

This will be essentially a topics course on applications of
complex manifold theory to arithmetic geometry, specifically Arakelov
Theory.
**Topics:**** **

- Forms
and
Currents on manifolds, currents associated to algebraic cycles
- equation and Green
Currents
- Review
of intersection theory on algebraic
varieties
- Arakelov’s
intersection theory on surfaces
- Arithmetic
Intersection theory in arbitrary
dimension
- Chern
classes, and Chern-Weil theory, Chern
forms of Hermitian holomorphic vector bundles on complex manifolds
- Secondary
characteristic classes and Bott-Chern
forms
- Chern
classes in arithmetic intersection theory
- Applications.
The amount of detail on applications will depend on the amount of
time
we have. The goal would be to
approach
some results such as the arithmetic Hilbert-Samuel formula,
and results of Vojta and Faltings in
Diophantine geometry.