Some Examples of Family Floer Mirrors

Abstract

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