2011•arXiv (Cornell University)Open access
The quest for counterexamples in toric geometry
Winfried Bruns
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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.
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