Laurent inversion

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Title: Laurent inversion
Authors: Coates, T
Kasprzyk, A
Prince, T
Item Type: Journal Article
Abstract: We describe a practical and effective method for reconstructing the deformation class of a Fano manifold X from a Laurent polynomial f that corresponds to X under Mirror Symmetry. We explore connections to nef partitions, the smoothing of singular toric varieties, and the construction of embeddings of one (possibly-singular) toric variety in another. In particular, we construct degenerations from Fano manifolds to singular toric varieties; in the toric complete intersection case, these degenerations were constructed previously by Doran--Harder. We use our method to find models of orbifold del Pezzo surfaces as complete intersections and degeneracy loci, and to construct a new four-dimensional Fano manifold.
Date of Acceptance: 11-Jun-2019
ISSN: 1558-8599
Publisher: International Press
Journal / Book Title: Pure and Applied Mathematics Quarterly
Copyright Statement: © 2019 The Authors.
Sponsor/Funder: Commission of the European Communities
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Commission of the European Communities
Funder's Grant Number: 240123
Keywords: math.AG
14J33 (Primary), 14J45, 52B20 (Secondary)
14J33 (Primary), 14J45, 52B20 (Secondary)
General Mathematics
0101 Pure Mathematics
0102 Applied Mathematics
Notes: 29 pages, 16 figures. This supersedes our earlier preprint with the same name (arXiv:1505.01855 [math.AG]). The new version is much more systematic, and works beyond the toric complete intersection case; it also draws connections to the work of Doran--Harder on amenable collections and Batyrev--Borisov on nef partitions
Appears in Collections:Pure Mathematics

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