Math 676: Moduli Spaces
WHEN: MWF 3 – 3:50 pm
WHERE: ENGRG E 204
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:
- The construction of a moduli space.
- Local/global coordinates on a moduli space.
- How to compactify a moduli space in a meaningful way.
- What alternative compactifications can one have.
- 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.