In this article, we show that some semi-rigid ÎĽ-stable sheaves on a
projective K3 surface X with Picard number 1 are stable in the sense of
Bridgeland's stability condition. As a consequence of our work, we show that
the special set U(X) \subset \Stab (X) reconstructs X itself. This gives a
sharp contrast to the case of an abelian surface.Comment: 31 pages, 2 figures. Claim 4.3 was deleted and added some
references;v3. some typos were correcte