## Kyoto Journal of Mathematics

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

Kotaro Kawatani

#### 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.

#### Article information

Source
Kyoto J. Math., Volume 53, Number 3 (2013), 597-627.

Dates
First available in Project Euclid: 19 August 2013

https://projecteuclid.org/euclid.kjm/1376917627

Digital Object Identifier
doi:10.1215/21562261-2265905

Mathematical Reviews number (MathSciNet)
MR3102563

Zentralblatt MATH identifier
1337.14017

#### Citation

Kawatani, Kotaro. Stability of Gieseker stable sheaves on K3 surfaces in the sense of Bridgeland and some applications. Kyoto J. Math. 53 (2013), no. 3, 597--627. doi:10.1215/21562261-2265905. https://projecteuclid.org/euclid.kjm/1376917627

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