722 research outputs found
Gorenstein toric Fano varieties
We investigate Gorenstein toric Fano varieties by combinatorial methods using
the notion of a reflexive polytope which appeared in connection to mirror
symmetry. The paper contains generalisations of tools and previously known
results for nonsingular toric Fano varieties. As applications we obtain new
classification results, bounds of invariants and formulate conjectures
concerning combinatorial and geometrical properties of reflexive polytopes.Comment: AMS-LaTeX, 29 pages with 5 figure
Quantum Cohomology Rings of Toric Manifolds
We compute the quantum cohomology ring of
an arbitrary -dimensional smooth projective toric manifold associated with a fan . The multiplicative structure of
depends on the choice of an element
in the ordinary cohomology group .
There are many properties of the quantum cohomology rings which are supposed to be valid for quantum cohomology
rings of K\"ahler manifoldsComment: 23 pages, Late
Algebraic Topology of Calabi-Yau Threefolds in Toric Varieties
We compute the integral homology (including torsion), the topological
K-theory, and the Hodge structure on cohomology of Calabi-Yau threefold
hypersurfaces and complete intersections in Gorenstein toric Fano varieties.
The methods are purely topological
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