Gorenstein toric Fano varieties
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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.
AMS-LaTeX, 29 pages with 5 figures
- University of Tübingen Germany
toric variety, 14J45, Fano variety, 52B20, 14J45; 14M25; 52B20, Mathematics - Algebraic Geometry, Fano varieties, Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry), lattice polytope, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Toric varieties, Newton polyhedra, Okounkov bodies, 14M25, Algebraic Geometry (math.AG)
toric variety, 14J45, Fano variety, 52B20, 14J45; 14M25; 52B20, Mathematics - Algebraic Geometry, Fano varieties, Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry), lattice polytope, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Toric varieties, Newton polyhedra, Okounkov bodies, 14M25, Algebraic Geometry (math.AG)
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