Stability of Gieseker stable sheaves on K3 surfaces in the sense of Bridgeland and some applications

Abstract

We show that some Gieseker stable sheaves on a projective K3 surface $X$ are stable with respect to a stability condition of Bridgeland on the derived category of $X$ if the stability condition is in explicit subsets of the space of stability conditions depending on the sheaves. Furthermore we shall give two applications of the result. As a part of these applications, we show that the fine moduli space of Gieseker stable torsion free sheaves on a K3 surface with Picard number one is the moduli space of $\mu$-stable locally free sheaves if the rank of the sheaves is not a square number.

arXiv comment34 pages, v2:we added one figure in page 23

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