1. CJM Online first
|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 curves
2. 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 varieties.
Keywords:toric, Fano, threefold, canonical singularities, convex polytopes
Categories:14J30, 14J30, 14M25, 52B20