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Stability conditions on K3 surfaces via mass of spherical objects

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arxiv 2504.12253 v1 pith:2SKYGB7R submitted 2025-04-16 math.AG math.GT

Kohei Kikuta , Naoki Koseki , Genki Ouchi This is my paper · ORCID
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keywords stabilitysphericalconditionsobjectsactionassociatedbapat-deopurkar-licatabroomhead-pauksztello-ploog-woolf
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abstract

We prove that a stability condition on a K3 surface is determined by the masses of spherical objects up to a natural $\mathbb{C}$-action. This is motivated by the result of Huybrechts and the recent proposal of Bapat-Deopurkar-Licata on the construction of a compactification of a stability manifold. We also construct lax stability conditions in the sense of Broomhead-Pauksztello-Ploog-Woolf associated to spherical bundles.

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  1. The Thurston compactification of the stability manifold of a generic analytic K3 surface

    math.AG 2025-05 accept novelty 6.0 of 10

    For an analytic K3 surface with Picard group zero, the mass map from the projective stability manifold to the space of masses of semi-rigid objects is a homeomorphism onto an open disk whose closure is a closed disk.

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