Contractibility of the geometric stability manifold of a surface

Nick Rekuski

Contractibility of the geometric stability manifold of a surface

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arxiv 2310.10499 v2 pith:JYEVU3OF submitted 2023-10-16 math.AG

Nick Rekuski This is my paper · ORCID

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keywords manifoldstabilitygeometriccontractiblesurfaceassociatedcomplexcontractibility

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Using a recent description of the geometric stability manifold, we show the geometric stability manifold associated to any smooth projective complex surface is contractible. We then use this result to demonstrate infinitely many new families of surfaces whose stability manifold is contractible.

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A Real Reduction of the Manifold of Bridgeland Stability Conditions
math.AG 2025-06 accept novelty 7.0 of 10

A quotient of the stability manifold by an equivalence relation is a real manifold of half dimension, and the original manifold can be reconstructed from the quotient together with the relation ≲.

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