Construction of the Hilbert Scheme (Fall 1999)
These are some notes from a course on "conjectures in algebraic geometry." My original goal was to construct the Hilbert scheme, talk about Goettshe's conjecture, construct the moduli space of curves, talk about Faber's conjectures, construct moduli spaces of stable maps, and finally talk about the Virasoro conjecture....all in one semester. Needless to say, I was too ambitious. I only succeeded in the first third. Here are the notes on how to construct the Hilbert scheme if you are ever stuck in the wilderness, with only Hartshorne as your guidebook.