Flat surfaces and stability structures
Algebraic Geometry
2020-09-08 v2 Representation Theory
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.
Cite
@article{arxiv.1409.8611,
title = {Flat surfaces and stability structures},
author = {Fabian Haiden and Ludmil Katzarkov and Maxim Kontsevich},
journal= {arXiv preprint arXiv:1409.8611},
year = {2020}
}
Comments
67 pages, 7 figures, v2: expanded from previous version following feedback, new title