Geometric Invariant Theory
Instructor Information
- Lecturer:Swarnava Mukhopadhyay
- Office:
MTH
4416
- Email: swarnava@umd.edu
- Phone: (301) 405-5156
Topics Covered
For useful references for these class, please look at this document. The most important and useful reference for this class is Peter Newstead's Tata Institute Lectures on
"Introduction to Moduli Problems and Orbit Spaces." Unfortunately the book might not be easily available in print. Briefly I will try to cover the following:
- What is GIT and what are the issues in taking quotients in algebraic geometry ? Brief
discussion o Categories, Functors and Yoneda Lemma. Detailed discussion of what is a
moduli problem ? Examples of fine moduli spaces, coarse moduli spaces and how we can
use GIT in moduli problems.
- Affine Quotients and Projective Quotients with many elementary examples. Criterion for
Stability (Hilbert-Mumford Criterion). Many examples of calculation of stability conditions
will be discussed. This is one of the main goals of this course. A good self-contained quide to these topics are lectures notes by
M. S. Narasimhan.
- Moduli Problems: Construction of the moduli of vector bundles over a curve of fixed rank
and degree M(r, d). Picard group of M(r, d). Construction of the moduli space of curves of
genus g.
- Variation of GIT for quotients of Toric varieties.
Exercise Sheet