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

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

2011-03-21

arxiv.org/abs/1103.3921v2

Mathematics

Algebraic Geometry

34 pages, v2:we added one figure in page 23

Scientific paper

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.

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