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December 2012 Stability conditions and $\mu$-stable sheaves on K3 surfaces with Picard number one
Kotaro Kawatani
Osaka J. Math. 49(4): 1005-1034 (December 2012).

Abstract

In this article, we show that some semi-rigid $\mu$-stable sheaves on a projective K3 surface $X$ with Picard number $1$ are stable under Bridgeland's stability condition. As a consequence of our work, we show that the special set $U(X) \subset \mathrm{Stab}(X)$ introduced by Bridgeland reconstructs $X$ itself. This gives a sharp contrast to the case of an abelian surface.

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Kotaro Kawatani. "Stability conditions and $\mu$-stable sheaves on K3 surfaces with Picard number one." Osaka J. Math. 49 (4) 1005 - 1034, December 2012.

Information

Published: December 2012
First available in Project Euclid: 19 December 2012

zbMATH: 1267.14025
MathSciNet: MR3007952

Subjects:
Primary: 14F05 , 14J28 , 18E30

Rights: Copyright © 2012 Osaka University and Osaka City University, Departments of Mathematics

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Vol.49 • No. 4 • December 2012
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