Math 676: Moduli Spaces




WHEN: MWF 3 – 3:50 pm


WHAT: geometry and intersection theory of moduli spaces of configuration of points on rational curves.

     Moduli spaces are ubiquitous and overwhelmingly important objects in mathematics. The idea is to establish a fruitful dictionary between the geometric properties of a collection of objects we want to study, and the geometry of a space whose points are in bijection with such geometric objects. We will use as a very concrete example the collection of moduli spaces of equivalence classes of rational pointed curves. This will allow us to mantain our discussion fairly concrete, as we address some pretty serious mathematical issues such as:

  1. The construction of a moduli space.
  2. Local/global coordinates on a moduli space.
  3. How to compactify a moduli space in a meaningful way.
  4. What alternative compactifications can one have.
  5. How to study intersection theory on a moduli space. 

Write up exercises 1-15 in the section on psi classes on manuscripta. Due Oct 31st.



1·        J.Kock, I. Vainsencher. An Invitation to Quantum Cohomology.

2·        J.Harris, I.Morrison. The moduli space of Curves.

3·        Kentaro Hori, Sheldon Katz, Albrecht Klemm, Rahul Pandharipande, Richard Thomas, Ravi Vakil, Eric Zaslow. Mirror Symetry.



1·        S. Keel. Intersection Theory of Moduli Space of Stable N-Pointed Curves of Genus Zero.