Tropical Realization Spaces and Tropical Approximations
Eric Katz · arXiv (Cornell University) · 2010
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.