Laurent inversion

Coates, Tom; Kasprzyk, Alexander; Prince, Thomas

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.

Citation

Coates, T., Kasprzyk, A., & Prince, T. (2019). Laurent inversion. Pure and Applied Mathematics Quarterly, 15(4), 1135–1179. https://doi.org/10.4310/PAMQ.2019.v15.n4.a5

• Journal Article Type: Article
• Acceptance Date: May 19, 2019
• Online Publication Date: Mar 20, 2020
• Publication Date: 2019
• Deposit Date: Jul 9, 2019
• Publicly Available Date: Jul 10, 2019
• Journal: Pure and Applied Mathematics Quarterly
• Print ISSN: 1558-8599
• Electronic ISSN: 1558-8602
• Publisher: International Press
• Peer Reviewed: Peer Reviewed
• Volume: 15
• Issue: 4
• Pages: 1135–1179
• DOI: https://doi.org/10.4310/PAMQ.2019.v15.n4.a5
• Keywords: Mirror symmetry, Fano manifolds, Toric degenerations
• Public URL: https://nottingham-repository.worktribe.com/output/2289298
• Publisher URL: https://www.intlpress.com/site/pub/pages/journals/items/pamq/content/vols/0015/0004/a005/index.php
• Contract Date: Jul 9, 2019