2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78412There 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 $k((z)) \oplus k((z))$. 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.14 pages, LaTex. To appear as the Abdus Salam International Centre for Theoretical Physics preprintAlgebraic Geometrytext