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Search: All articles in the CJM digital archive with keyword Fano

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1. CJM 2016 (vol 68 pp. 784)

Doran, Charles F.; Harder, Andrew
 Toric Degenerations and Laurent Polynomials Related to Givental's Landau-Ginzburg Models 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 varietiesCategories:14M25, 14J32, 14J33, 14J45

2. CJM 2014 (vol 67 pp. 667)

Nishinou, Takeo
 Toric Degenerations, Tropical Curve, and Gromov-Witten Invariants of Fano Manifolds In this paper, we give a tropical method for computing Gromov-Witten type invariants of Fano manifolds of special type. This method applies to those Fano manifolds which admit toric degenerations to toric Fano varieties with singularities allowing small resolutions. Examples include (generalized) flag manifolds of type A, and some moduli space of rank two bundles on a genus two curve. Keywords:Fano varieties, Gromov-Witten invariants, tropical curvesCategory:14J45

3. CJM 2010 (vol 62 pp. 1293)

Kasprzyk, Alexander M.
 Canonical Toric Fano Threefolds An inductive approach to classifying all toric Fano varieties is given. As an application of this technique, we present a classification of the toric Fano threefolds with at worst canonical singularities. Up to isomorphism, there are $674,\!688$ such varieties. Keywords:toric, Fano, threefold, canonical singularities, convex polytopesCategories:14J30, 14J30, 14M25, 52B20
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