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

Doran, Charles F. ; Harder, Andrew

Canadian journal of mathematics, Tome 68 (2016) no. 4, pp. 784-815

Résumé

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.

Détail

DOI : 10.4153/CJM-2015-049-2

Mots-clés : 14M25, 14J32, 14J33, 14J45, Fano varieties, Landau-Ginzburg models, Calabi-Yau varieties, toric varieties

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