Yi Hu, Math 538, Fall 2005
Section MW 2:00pm 3:15 pm, or any other available time
Instructor: Yi Hu
Office Hours: MW 3:30-5:00 or by appointment
Office: Room 616, Math Building
Phone: 621-4397
E-mail: yhu@math.arizona.edu
Title: Introduction to Geometric Invariant Theory and Moduli Spaces
Text: I will distribute my own lecture notes.
References: Igor Dolgachev, Lecture on Invariant Theory. Cambridge
University Press. P. E. Newstead, Introduction to Moduli Problems and
Orbit Spaces, Tata Institute, 1978. Mumford et el, Geometric Invariant
Theory, 3rd edition, Springer-Verlag, 1994.
Homework: Homework or projects will be assigned but not
collected. Selected homework will be discussed in class.
Description: I will start from the very beginning, reviewing algebraic
varieties, algebraic groups, group actions, and introducing the basics
of the quotient theory in algebraic geometry, the Geometric Invariant
Theory. Along the way, I will also introduce symplectic reduction in
symplectic geometry. The two theories are beautifully linked by the
theory of moment map. Finally, some fundamental and important moduli
spaces will be introduced, this will, at least, include M_{0,n}, the
moduli space of stable n-pointed rational curves. The course will
emphasize intuition behind the deep theory, using many interesting and
useful examples.
Prerequisites: Any one-semester course on algebraic geometry, or 536A,
or the equivalent.