The quest for counterexamples in toric geometry

Abstract

We discuss an experimental approach to open problems in toric geometry: are smooth projective toric varieties (i) projectively normal and (ii) defined by degree 2 equations? We discuss the creation of lattice polytopes defining smooth toric varieties as well as algorithms checking properties (i) and (ii) and further potential properties, in Particular a weaker version of (ii) asking for scheme-theoretic definition in degree 2.

Funal version with small corrections and updated references

References in corpus (2)

• Constructive degree bounds for group-based models
• Projective normality of nonsingular toric varieties of dimension three

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