Tropical Realization Spaces and Tropical Approximations

Details Tropical Realization Spaces and Tropical Approximations Tropical Realization Spaces and Tropical Approximations

2010-08-11

arxiv.org/abs/1008.1836v1

Mathematics

Algebraic Geometry

Scientific paper

Tropicalization is a procedure that assigns polyhedral complexes to algebraic subvarieties of a torus. We construct tropical realization spaces parameterizing varieties with a particular polyhedral complex as their tropicalization. They are constructed as an admissible open in the analytification of an appropriate Hilbert scheme. We also prove a sort of tropical Lefschetz principle which can be used to extend analytic proofs in tropical geometry to formal families.

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