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

D. V. Osipov
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Abstract

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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D. V. Osipov. 1999-04-27. Stability of torsion free sheaves on curves and infinite-dimensional Grassmanian manifold. https://arxiv.org/abs/math/9904152

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