Lectures in Geometric Invariant theory, spring 2003

• February 3, Monday : I covered most of chapters 1-3 of the script, except for the proof that the discriminant is invariant.
• February 5, Wednesday : Proved that the discriminant of a binary form is invariant under SL(2,C). Started on affine varieties, discussed Hilberts basis theorem and Nullstellensatz.
• February 10, Monday : Did most of chapter 5, but got into troubles when explaining what the regular functions on a quasi-affine variety are.
• Feburary 12, Wednesday : Gave a better account of quasi-affine varieties, including the fact that invariant rings behave right with respect to passage to open subsets.
• February 17, Monday : Discussed linearly reductive groups. Proved using Haar measure and a variation on Weyl's unitary trick that GL(n,C) is linearly reductive.
• February 19, Wednesday: Started on the discussion of the Omega process, to give an algebraic proof that GL_n is reductive.
• February 24, Monday : Finished the Omega process, defined good quotients and got as far as the formulation of Hilbert 14th problem for reductive groups.
• February 26 Wednesday : Proved Hilbert 14.
• March 3 Monday : Existence of good quotients in the affine case. Projective spaces
• March 5 Wednesday : Twisted projective spaces.
• March 10 Monday : Being good is a local property. A good quotient is a categorical quotient in the category of projective varieties.
• March 12 Wedensday : Proof of existence of good quotients in the projective case.
• March 24 Monday : No lecture (Am at conference)
• March 26 Wednesday : No lecture (Am still at conference)
• April 16 Wedesday : No lecture. Birthday of the queen.
• April 21 Monday : No lecture. Easter Monday.