Rational curves in the plane

Meetings

1. 15/4-24: Introduction, The number of rational cubics through 8 points, Notes, Problems

2. 22/4-24: Quadruples, cross ratios, Introduction to moduli spaces and universal families (Section 0.1 and 1.1 of [KV], Section 0.2 own reading) Notes, Problems

3. 6/5-24: n-pointed rational curves, stable curves, Notes, Problems

4. 13/5-24: Stabilization, contraction, construction of the moduli space of stable rational n-pointed curves, Notes, Problems

5. 4/6-24: The boundary of M_{0,n}, No problem set but list boundary components for small values of n until you feel comfortable

6. 13/6-24: Stable maps, Problems

7. 20/6-24: Moduli of stable maps, Kontsevich's formula, Problems

References:

[KV] Kock, Vainsencher - "An invitation to quantum cohomology"
[FP] Fulton, Pandharipande - "Notes on stable maps and quantum cohomology"
[EGH] Eisenbud, Green, Harris - "Cayley-Bacharach theorems and conjectures"
[M] Miranda - "Linear systems of plane curves"
[H] Hartshorne - "Algebraic geometry"
[Ke] Keel - "Intersection theory of moduli space of stable n-pointed curves of genus 0"
[Ka] Kapranov - "Chow quotients of Grassmannian I"