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Gorenstein toric Fano varieties

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arxiv math/0405448 v1 pith:GLZ5BBNI submitted 2004-05-24 math.AG math.CO

Benjamin Nill This is my paper · ORCID
classification math.AGmath.CO
keywords fanotoricvarietiescombinatorialgorensteinreflexiveresultsappeared
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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.

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  1. Fano and Reflexive Polytopes from Feynman Integrals

    hep-th 2025-12 unverdicted novelty 6.0 of 10

    Quasi-finite Feynman integrals produce sparse Fano and reflexive polytopes that encode degenerate Calabi-Yau varieties and link to del Pezzo surfaces, K3 surfaces, and Calabi-Yau threefolds.

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