1. CJM 2016 (vol 68 pp. 784)
||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 varieties
Categories:14M25, 14J32, 14J33, 14J45
2. CJM 2014 (vol 67 pp. 667)
||Toric Degenerations, Tropical Curve, and Gromov-Witten Invariants of Fano Manifolds|
In this paper, we give a tropical method for computing Gromov-Witten
of Fano manifolds of special type.
This method applies to those Fano manifolds which admit toric
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 curves
3. CJM 2010 (vol 62 pp. 1293)
||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
Keywords:toric, Fano, threefold, canonical singularities, convex polytopes
Categories:14J30, 14J30, 14M25, 52B20