Back to Algebraic Geometry Seminar: Spring 2008
Algebraic Geometry Seminar
Date: Wednesday, Jan 9, 2008
Time: 3:30PM - 4:30PM
Location: LCB 323
LCB 215
Andrew Snowden
Princeton University
Title |
The equations of the GIT quotient (P 1 ) n /PGL(2) |
Abstract |
Let n >= 4 be an even integer and let M n be the moduli space of n points on P 1 modulo the action of PGL(2), thought of as the GIT quotient (P 1 ) n /PGL(2). The space M n has a natural projective embedding; let R n be its projective coordinate ring. The ring R n was studied classically in the context of invariant theory. In the late nineteenth centruy, Kempe proved that R n is generated by its degree one piece. Since that time however, generators for the ideal of relations have not been determined. I will talk about my recent work with Howard, Millson and Vakil towards understanding generators of this ideal. Two of our results: 1) the ideal of relations is always generated in degrees <= 3; and 2) for all n not equal to 6 the image of M n in projective space is cut out by quadrics. |
Algebraic Geometry