S-equivalence

S-equivalence is an equivalence relation on the families of semistable vector bundles on an algebraic curve.
Definition.
Let "X" be a projective curve over an algebraically closed field "k". A vector bundle on "X" can be considered as a locally free sheaf. Every semistable locally free "E" on "X" admits a Jordan-Hölder filtration with stable subquotients, i.e.
where formula_2 are locally free sheaves on "X" and formula_3 are stable. Although the Jordan-Hölder filtration is not unique, the subquotients are, which means that formula_4 is unique up to isomorphism.
Two semistable locally free sheaves "E" and "F" on "X" are "S"-equivalent if "gr E" ≅ "gr F".