Flat surfaces and stability structures

Author: 

Haiden, F
Katzarkov, L
Kontsevich, M

Publication Date: 

21 November 2017

Journal: 

Publications mathématiques de l'IHÉS

Last Updated: 

2021-04-29T20:06:13.687+01:00

Issue: 

1

Volume: 

126

DOI: 

10.1007/s10240-017-0095-y

page: 

247-318

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.

Symplectic id: 

1040587

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article