Math 191:
Geometric Invariant Theory and moduli spaces
Lectures: 10:30--12:00 on Tuesday and
Thursday
Instructor: Amin Gholampour
Email address: agholamp@caltech.edu
Office: Sloan 258
Office hour: Any time you find me in the office
Course description: The course will
discuss geometric invariant theory (GIT) and its application to the construction
of Moduli spaces. GIT has been successfully applied to the construction of
moduli space of curves, vector bundles, abelian varieties and many other objects
in algebraic geometry. We will start with some examples to illustrate the main
ideas and continue with the notion of stability. We will then apply GIT to the
construction of moduli space of curves and vector bundles over curves, and shall
discuss other applications if time allows.
References:
Shigeru Mukai, An introduction to
invariants and moduli.
David Mumford, John Fogarty, and Frances
Kirwan, Geometric invariant theory.
Joe Harris and Ian Morrison,
Moduli of curves.
Barbara Fantechi et al., Fundamental Algebraic Geometry,
Moduli of curves.
More may be added to this list.
Course Policy:
There will be sporadic assigned homework. And also seminars at the end of
the quarter for those who are interested in working on a related topic.