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

  Published:2016-04-18
 Printed: Aug 2016
  • Charles F. Doran,
    Department of Mathematical and Statistical Sciences, 632 CAB, University of Alberta, Edmonton, Alberta T6G 2G1, Canada
  • Andrew Harder,
    Department of Mathematical and Statistical Sciences, 632 CAB, University of Alberta, Edmonton, Alberta T6G 2G1, Canada
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Abstract

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: Fano varieties, Landau-Ginzburg models, Calabi-Yau varieties, toric varieties Fano varieties, Landau-Ginzburg models, Calabi-Yau varieties, toric varieties
MSC Classifications: 14M25, 14J32, 14J33, 14J45 show english descriptions Toric varieties, Newton polyhedra [See also 52B20]
Calabi-Yau manifolds
Mirror symmetry [See also 11G42, 53D37]
Fano varieties
14M25 - Toric varieties, Newton polyhedra [See also 52B20]
14J32 - Calabi-Yau manifolds
14J33 - Mirror symmetry [See also 11G42, 53D37]
14J45 - Fano varieties
 

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