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Toric Degenerations and Laurent Polynomials Related to Givental's Landau–Ginzburg Models

Published online by Cambridge University Press:  20 November 2018

Charles F. Doran  and
Andrew Harder
Charles F. Doran
Affiliation:
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G 2G1 e-mail: charles.doran@ualberta.caaharder@ualberta.ca
Andrew Harder
Affiliation:
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G 2G1 e-mail: charles.doran@ualberta.caaharder@ualberta.ca
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Abstract

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For an appropriate class of Fano complete intersections in toric varieties, we prove that there is a concrete relationship between degenerations to specific toric subvarieties and expressions for Givental's Landau–Ginzburg models as Laurent polynomials. As a result, we show that Fano varieties presented as complete intersections in partial flag manifolds admit degenerations to Gorenstein toric weak Fano varieties, and their Givental Landau–Ginzburg models can be expressed as corresponding Laurent polynomials.

We also use this to show that all of the Laurent polynomials obtained by Coates, Kasprzyk and Prince by the so–called Przyjalkowski method correspond to toric degenerations of the corresponding Fano variety. We discuss applications to geometric transitions of Calabi–Yau varieties.

Keywords

14M2514J3214J3314J45Fano varietiesLandau-Ginzburg modelsCalabi-Yau varietiestoric varieties
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 68 , Issue 4 , 01 August 2016 , pp. 784 - 815
Copyright
Copyright © Canadian Mathematical Society 2016

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