490 research outputs found
Some Examples of Family Floer Mirrors
In this article, we give explicit calculations for the family Floer mirrors
of some non-compact Calabi-Yau surfaces. We compare it with the mirror
construction of Gross-Hacking-Keel for suitably chosen log Calabi-Yau pairs and
the rank two cluster varieties of finite type. In particular, the
analytifications of the later two give partial compactifications of the family
Floer mirrors that we computed.Comment: 38 pages, 15 figures, comments are welcom
Cluster scattering diagrams and theta functions for reciprocal generalized cluster algebras
We give a construction of generalized cluster varieties and generalized
cluster scattering diagrams for reciprocal generalized cluster algebras, the
latter of which were defined by Chekhov and Shapiro. These constructions are
analogous to the structures given for ordinary cluster algebras in the work of
Gross, Hacking, Keel, and Kontsevich. As a consequence of these constructions,
we are also able to construct theta functions for generalized cluster algebras,
again in the reciprocal case, and demonstrate a number of their structural
properties.Comment: Updated to reflect reviewers' comments and to use the preferred
journal formattin
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