Stability of torsion free sheaves on curves and infinite-dimensional Grassmanian manifold

الأصل · EN

There exists the Krichever map from the set of quintets (C,p,F,t,e) (where C is an integral and complete algebraic curve, p a smooth rational point, F a rank 2 torsion free coherent sheaf on C, t a local formal parameter in p and e a formal trivialization of F around p) to the infinite Grassmanian of k((z)) ⊕ k((z)). We describe the images of quintets with (semi)stable sheaves F in terms of Plucker coordinates and get some analog of GIT Hilbert-Mumford numerical criterion with respect to actions of some 1-parametric subgroups of the group SL(2,k[[z]]) on the determinant bundle of the infinite Grassmanian.