Toric Degenerations and Laurent Polynomials Related to Givental's Landau-Ginzburg Models
Printed: Aug 2016
Charles F. Doran,
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.
Fano varieties, Landau-Ginzburg models, Calabi-Yau varieties, toric varieties
14M25 - Toric varieties, Newton polyhedra [See also 52B20]
14J32 - Calabi-Yau manifolds
14J33 - Mirror symmetry [See also 11G42, 53D37]
14J45 - Fano varieties