Flat surfaces and stability structures

2014/09/30 by Fabian Haiden, F. Haiden, Ludmil Katzarkov +3 · 5 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models

paper · doi:10.1007/s10240-017-0095-y

crossref issued 2017/11/07 · crossref published 2017/11/07 · crossref published-online 2017/11/07 · openalex publication_date 2017/11/07 · crossref created 2017/11/21 · openalex created_date 2025/10/10 · crossref deposited 2026/02/17 · crossref indexed 2026/07/30 · openalex updated_date 2026/07/31

Abstract

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.

Citations

• Vector Bundles Over an Elliptic Curve
• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations

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