Let G be a complex reductive group acting algebraically on a complex projective variety X . Given a polarisation of X , i.e., an ample G-line bundle L over X , Mumford (see [M-F-K]) defined the notion of stability: A point x ∈ X is said to be semistable with respect to L if and only if there exits m ∈ N and an invariant section s : X → L such that s(x) 6= 0. Let X(L) denote the set of semistabl...

Given a representation of compact Lie group and state we define probability measure on the coadjoint orbits dominant weights by considering decomposition into irreducible components. For large tensor powers independent copies show that induced distributions converge to value moment map. faithful states prove measures satisfy deviation principle with an explicitly given rate function.

In this paper, we study the moment map image of algebraic curves in toric surfaces. We are particularly interested in the situations that we are able to perturb the moment map so that the moment map image of the algebraic curve is a graph. To put our problem into proper context, let’s start with CP. Consider the natural real n-torus (T ) action on CP given by e(x) = (ex1, e x2, · · · , exn). Pa...