Toric degenerations and Laurent polynomials related to Givental's Landau-Ginzburg models

Charles F. Doran, Andrew Harder

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)784-815
Number of pages32
JournalCanadian Journal of Mathematics
Issue number4
StatePublished - Aug 2016
Externally publishedYes


  • Calabi-Yau varieties
  • Fano varieties
  • Landau-Ginzburg models
  • Toric varieties

ASJC Scopus subject areas

  • Mathematics(all)


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