Math 571 Advanced Topics in Algebraic Geometry: Moduli Spaces

Welcome to Math 571! This course is an introduction to moduli spaces. In the first half of the course we will construct moduli spaces that are central to Algebraic Geometry such as Hilbert schemes, moduli spaces of curves and the Kontsevich moduli spaces of stable maps. The second half of the course will be devoted to studying the geometry of the moduli spaces of curves and stable maps. We will discuss the intersection theory, the cohomology, the tautological ring and the birational geometry of these moduli spaces.

Lecturer: Izzet Coskun, coskun@math.uic.edu

Office hours: F 11--12, 1:30--3:00 and by appointment in SEO 423

Time: MWF 9:00--9:50 am

Venue: Taft Hall 316

Text book: The text book for this course is Moduli of Curves by Joe Harris and Ian Morrison (GTM 187, Springer, 1998). The text book will be supplemented by lecture notes.

Prerequisites: Algebraic Geometry at the level of Chapters 2 and 3 of Hartshorne or Chapters 0 and 1 of Griffiths and Harris.

Homework: I will regularly give homework. You are strongly encouraged to do the homework.

Grading: Your grade will be based entirely on homework (100%).

Course materials: (Grassmannian)

(Hilbertschemes1)

(Moduli of Curves 1)

(Homology of Moduli of Curves 1)

Sample Grothendieck-Riemann-Roch calculations. Read at your own peril! (GRR calculations)