A hyperbolic structure and stability conditions on K3 surfaces with ρ=1

Details A hyperbolic structure and stability conditions on K3 surfaces with ρ=1 A hyperbolic structure and stability conditions on K3 surfaces with ρ=1

2012-04-05

arxiv.org/abs/1204.1128v1

Mathematics

Algebraic Geometry

28 pages, 3 figures

Scientific paper

In this article we introduce a hyperbolic structure on the (normalized) space of stability conditions on projective K3 surfaces X with Picard rank \rho (X) =1. And we show that all walls are geodesic in the normalized space with respect to the hyperbolic structure. Furthermore we demonstrate how the hyperbolic structure is helpful for us by discussing mainly two topics. We first make a study of so called Bridgeland's conjecture. In the second topic we prove a famous Orlov's theorem without the global Torelli theorem.

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