Kyoto Journal of Mathematics
- Kyoto J. Math.
- Volume 53, Number 3 (2013), 597-627.
Stability of Gieseker stable sheaves on K3 surfaces in the sense of Bridgeland and some applications
We show that some Gieseker stable sheaves on a projective K3 surface are stable with respect to a stability condition of Bridgeland on the derived category of 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 -stable locally free sheaves if the rank of the sheaves is not a square number.
Kyoto J. Math., Volume 53, Number 3 (2013), 597-627.
First available in Project Euclid: 19 August 2013
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14F05: Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20] 14J28: $K3$ surfaces and Enriques surfaces
Secondary: 14J60: Vector bundles on surfaces and higher-dimensional varieties, and their moduli [See also 14D20, 14F05, 32Lxx] 14J10: Families, moduli, classification: algebraic theory
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