Gorenstein toric Fano varieties

By Benjamin Nill. 2004

103 citations recorded by the source corpus.

Abstract.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 generalizations 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.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/a85258c1e91196aba0a3c69ca1c0b2bca1dd46fd

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

Citations in the corpus

Canonical Toric Fano Threefolds (2008, unknown): “Consult, for example, [KS97, Sat00, PRV00, Nil05 ].”
The Reflexive Dimension of a Lattice Polytope (2004, background): “They enjoy a variety of interesting combinatorial properties [4, 11] which are not well understood.”
An algorithm for the classification of smooth Fano polytopes (2007, background): “5 When F is a facet and v a vertex of a smooth Fano d-polytope P , such that 〈uF , v〉 = 0, we can say something about the face lattice of P .”
Asymptotically cylindrical Calabi–Yau 3–folds from weak Fano 3–folds (2012, methodology): “Every Gorenstein toric Fano variety X has an associated combinatorial object called a reflexive polytope which determines X ; see Chapters 1 and 2 in the thesis of Nill [76] for a review of basic definitions and facts in toric Fano geometry.”