Stability conditions and $μ$-stable sheaves on K3 surfaces with Picard number one

Details Stability conditions and $μ$-stable sheaves on K3 surfaces with Picard number one Stability conditions and $μ$-stable sheaves on K3 surfaces with Picard number one

2010-05-21

arxiv.org/abs/1005.3877v3

Mathematics

Algebraic Geometry

31 pages, 2 figures. Claim 4.3 was deleted and added some references;v3. some typos were corrected

Scientific paper

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

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