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The 3-dimensional Lyness map and a self-mirror log Calabi–Yau 3-fold

Ducat, Tom

The 3-dimensional Lyness map and a self-mirror log Calabi–Yau 3-fold Thumbnail


Authors

Tom Ducat



Abstract

The 2-dimensional Lyness map is a 5-periodic birational map of the plane which may famously be resolved to give an automorphism of a log Calabi–Yau surface, given by the complement of an anticanonical pentagon of (-1)-curves in a del Pezzo surface of degree 5. This surface has many remarkable properties and, in particular, it is mirror to itself. We construct the 3-dimensional big brother of this surface by considering the 3-dimensional Lyness map, which is an 8-periodic birational map. The variety we obtain is a special (non-Q-factorial) affine Fano 3-fold of type V12, and we show that it is a self-mirror log Calabi–Yau 3-fold.

Citation

Ducat, T. (2024). The 3-dimensional Lyness map and a self-mirror log Calabi–Yau 3-fold. manuscripta mathematica, 174(1-2), 87-140. https://doi.org/10.1007/s00229-023-01497-0

Journal Article Type Article
Acceptance Date Jun 30, 2023
Online Publication Date Aug 3, 2023
Publication Date May 1, 2024
Deposit Date Sep 20, 2023
Publicly Available Date Sep 20, 2023
Journal manuscripta mathematica
Print ISSN 0025-2611
Electronic ISSN 1432-1785
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 174
Issue 1-2
Pages 87-140
DOI https://doi.org/10.1007/s00229-023-01497-0
Keywords General Mathematics
Public URL https://durham-repository.worktribe.com/output/1743464

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