Topology/alg. Geometry Seminar
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چکیده
1PM: Oleg Viro (Stony Brook). Multifields (fields with multivalued addition), base fields of tropical geometries. Abstract:In many classical number sets (e.g., complex numbers, real numbers and non-negative real numbers), there are remarkable structures of multifield. Replacing the tropical max-plus semifield in the foundations of tropical geometry by a multifield simplifies the structure of tropical geometry and makes it closer to the classical parts of algebraic geometry. The multifield of complex numbers underlies a tropical complex geometry which bridges the gap between tropical and complex geometries. Nonsingular tropical complex varieties are topological manifolds homeomorphic to complex varieties but consisting of holomorphic, Lagrangian and mixed pieces. Amoebas of tropical complex varieties are usual tropical varieties.
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