Chennai Mathematical Institute


3.30pm,Lecture Hall 2
Moduli spaces of polygons and moduli spaces of labelled points: the real story

Priyavrat Deshpande
Chennai Mathematical Institute.


A polygon in the Euclidean space is a closed piece-wise linear path. Allowing the angles to change continuously one obtains the moduli space of polygons. Generically it is a compact complex manifold. It can also be realized either as a space of stable configurations of weighted points on the projective line or as a GIT quotient of the Grassmannian of 2-planes by the maximal torus. It is related to one more classical construction in algebraic geometry, the Deligne-Mumford compactification of of the space of n-pointed genus zero algebraic curves. By a result of Y. Hu the Deligne-Mumford compactification is an iterated blowup of the moduli space of polygons.

In this talk I will concentrate on the real points of the above two complex varieties. I will report on the ongoing work with Nachiketa Adhikari in which we are trying to understand the relationship between the real loci.