Violaxanthin de-epoxidase

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.

0 = E_{0} \subseteq E_{1} \subseteq \dots \subseteq E_{n} = E

where $E_{i}$ are locally free sheaves on X and $E_{i} / E_{i - 1}$ are stable. Although the JH-Filtration is not unique, the subquotients are, which means that $g r E = ⨁_{i} E_{i} / E_{i - 1}$ is unique up to isomorphism.

Two semistable locally free sheaves E and F on X are S-equivalent if gr E ≅ gr F.