Hyperbolic Structures and Root Systems
Gert Heckman, Eduard Looijenga
TL;DR
This paper explores the construction of complex hyperbolic structures on complements of toric mirror arrangements linked to simply laced root systems, identifying conditions for these structures to form ball quotients.
Contribution
It introduces a new family of complex hyperbolic structures on toric mirror arrangement complements and determines when these structures produce ball quotients.
Findings
Identification of parameter conditions for ball quotient structures
Construction of a one-parameter family of hyperbolic structures
Connection between root systems and complex hyperbolic geometry
Abstract
We discuss the construction of a one parameter family of complex hyperbolic structures on the complement of a toric mirror arrangement associated with a simply laced root system. Subsequently we find conditions for which parameter values this leads to ball quotients.
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