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

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

1999-04-27

arxiv.org/abs/math/9904152v1

Mathematics

Algebraic Geometry

14 pages, LaTex. To appear as the Abdus Salam International Centre for Theoretical Physics preprint

Scientific paper

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 $k((z)) \oplus k((z))$. 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.

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