1,026 research outputs found
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.Comment: 34 pages, v2:we added one figure in page 2
Stability conditions on morphisms in a category
Let be the homotopy category of a stable infinity
category . Then the homotopy category
of morphisms in the stable infinity
category is also triangulated. Hence the space of stability conditions on
is well-defined though the non-emptiness
of is not obvious. Our
basic motivation is a comparison of the homotopy type of
and that of
. Under the motivation we
show that functors and induce continuous maps from to
contravariantly where (resp. ) takes a morphism to the target
(resp. source) of the morphism. As a consequence, if
is nonempty then so is
. Assuming is
the derived infinity category of the projective line over a field, we further
study basic properties of and . In addition, we give an
example of a derived category which does not have any stability condition.Comment: 26 pages, comments are welcome. For v2, added subsection 2.2 which
gives a description of a Serre functor of the category of morphisms in
. For v3, the proof of Proposition 3.3 has been updated. For v5,
Section 6 was added. For v6, modified the proof of Proposition 6.1. For v7,
minor revision for Proposition 6.1, final versio
Stability conditions and -stable sheaves on K3 surfaces with Picard number one
In this article, we show that some semi-rigid -stable sheaves on a
projective K3 surface 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 itself. This gives a
sharp contrast to the case of an abelian surface.Comment: 31 pages, 2 figures. Claim 4.3 was deleted and added some
references;v3. some typos were correcte
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