Mirror symmetry, Laurent inversion, and the classification of {Q}-Fano threefolds
Author(s)
Coates, Tom
Heuberger, Liana
Kasprzyk, Alexander M
Type
Journal Article
Abstract
We describe recent progress in a program to understand the classification of three-dimensional Fano varieties with ℚ-factorial terminal singularities using mirror symmetry. As part of this we give an improved and more conceptual understanding of Laurent inversion, a technique that sometimes allows one to construct a Fano variety 𝑋 directly from a Laurent polynomial 𝑓 that corresponds to it under mirror symmetry.
Date Issued
2025-12-01
Date Acceptance
2025-04-21
Citation
Transactions of the London Mathematical Society, 2025, 12 (1)
ISSN
2052-4986
Publisher
Wiley
Journal / Book Title
Transactions of the London Mathematical Society
Volume
12
Issue
1
Copyright Statement
© 2025 The Author(s). Transactions of the London Mathematical Society is copyright © London Mathematical Society. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
License URL
Subjects
BOUNDEDNESS
DEL PEZZO SURFACES
EXISTENCE
LOGARITHMIC DEGENERATION DATA
Mathematics
MINIMAL MODELS
Physical Sciences
Q-FANO 3-FOLDS
Science & Technology
TOM
VARIETIES
Publication Status
Published
Article Number
e70012
Date Publish Online
2025-09-22