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Flat surfaces and stability structures

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arxiv 1409.8611 v2 pith:JGNSWT4K submitted 2014-09-30 math.AG math.RT

Fabian Haiden , Ludmil Katzarkov , Maxim Kontsevich This is my paper · ORCID
classification math.AGmath.RT
keywords surfacesstructurescategoriesspacesstabilityachievedalgebraappear
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We identify spaces of half-translation surfaces, equivalently complex curves with quadratic differential, with spaces of stability structures on Fukaya-type categories of punctured surfaces. This is achieved by new methods involving the complete classification of objects in these categories, which are defined in an elementary way. We also introduce a number of tools to deal with surfaces of infinite area, where structures similar to those in cluster algebra appear.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Topological model for derived category associated to sphere with four binaries

    math.RT 2026-07 conditional novelty 6.0 of 10

    Indecomposable rigid objects in the derived category of the (2,2,2,2)-weighted projective line are shown to correspond to graded simple arcs on a sphere with four binaries, with Hom-dimensions given by oriented inters...

  2. Contractibility and total semi-stability conditions of Euclidean quivers

    math.RT 2025-01 conditional novelty 6.0 of 10

    The moduli space of total semi-stability conditions on Euclidean quivers is described by partition data and contracts linearly to any non-concentrated stability condition.

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