Generalizing the Cross-ratio: The Moduli Space of N Points on the Projective <br/><br/>Line is Cut Out by Simple Quadrics if N is Not Six

Monday, September 18, 2006 - 9:30am - 10:20am
EE/CS 3-180
Ravi Vakil (Stanford University)
The cross-ratio is a classical gadget that let's you see if two
sets of four
points on the projective line are projectively equivalent

it is the
moduli space of four points on the projective line. The
generalization of
this to an arbitrary number of points leads to the notion of
the moduli space
of n points on the projective line, which is a projective
variety, one of the
most classical examples of a Geometric Invariant Theory
quotient. It also may
be interpreted as the space of all polygons in 3-space. We
show that this
space is actually cut out by quadrics, of a particularly simple
sort. This
talk is intended for a broad audience. (This is joint work
with B. Howard, J.
Millson, and A. Snowden, and deals with preprint