Publications

BibTex format

@article{Coates:2021:10.1098/rspa.2021.0584,
author = {Coates, T and Kasprzyk, AM and Pitton, G and Tveiten, K},
doi = {10.1098/rspa.2021.0584},
journal = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
pages = {1--21},
title = {Maximally mutable laurent polynomials},
url = {http://dx.doi.org/10.1098/rspa.2021.0584},
volume = {477},
year = {2021}
}

Download

RIS format (EndNote, RefMan)

TY  - JOUR
AB  - We introduce a class of Laurent polynomials, called maximally mutable Laurentpolynomials (MMLPs), that we believe correspond under mirror symmetry to Fanovarieties. A subclass of these, called rigid, are expected to correspond toFano varieties with terminal locally toric singularities. We prove that thereare exactly 10 mutation classes of rigid MMLPs in two variables; under mirrorsymmetry these correspond one-to-one with the 10 deformation classes of smoothdel~Pezzo surfaces. Furthermore we give a computer-assisted classification ofrigid MMLPs in three variables with reflexive Newton polytope; under mirrorsymmetry these correspond one-to-one with the 98 deformation classes ofthree-dimensional Fano manifolds with very ample anticanonical bundle. Wecompare our proposal to previous approaches to constructing mirrors to Fanovarieties, and explain why mirror symmetry in higher dimensions necessarilyinvolves varieties with terminal singularities. Every known mirror to a Fanomanifold, of any dimension, is a rigid MMLP.
AU  - Coates,T
AU  - Kasprzyk,AM
AU  - Pitton,G
AU  - Tveiten,K
DO  - 10.1098/rspa.2021.0584
EP  - 21
PY  - 2021///
SN  - 1364-5021
SP  - 1
TI  - Maximally mutable laurent polynomials
T2  - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
UR  - http://dx.doi.org/10.1098/rspa.2021.0584
UR  - http://arxiv.org/abs/2107.14253v1
UR  - https://royalsocietypublishing.org/doi/10.1098/rspa.2021.0584
UR  - http://hdl.handle.net/10044/1/91752
VL  - 477
ER  -

Download

ProfessorTomCoates

Contact

Location

Summary

Citation

BibTex format

RIS format (EndNote, RefMan)