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Title: Mirror Symmetry for Truncated Cluster Varieties
In the algebraic setting, cluster varieties were reformulated by Gross-Hacking-Keel as log Calabi-Yau varieties admitting a toric model. Building on work of Shende-Treumann-Williams-Zaslow in dimension 2, we describe the mirror to the GHK construction in arbitrary dimension: given a truncated cluster variety, we construct a symplectic manifold and prove homological mirror symmetry for the resulting pair. We also describe how our construction can be obtained from toric geometry, and we relate our construction to various aspects of cluster theory which are known to symplectic geometers.  more » « less
Award ID(s):
2001897
PAR ID:
10540211
Author(s) / Creator(s):
;
Corporate Creator(s):
;
Publisher / Repository:
SIGMA
Date Published:
Journal Name:
Symmetry, Integrability and Geometry: Methods and Applications
ISSN:
1815-0659
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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