First steps in tropical geometry

Details First steps in tropical geometry First steps in tropical geometry

2003-06-25

arxiv.org/abs/math/0306366v2

Mathematics

Algebraic Geometry

Revised version based on reviewers' comments; also corrected the statement of Theorem 2.6. To appear in Proc. Conference on Id

Scientific paper

Tropical algebraic geometry is the geometry of the tropical semiring $(\mathbb{R},\min,+)$. Its objects are polyhedral cell complexes which behave like complex algebraic varieties. We give an introduction to this theory, with an emphasis on plane curves and linear spaces. New results include a complete description of the families of quadrics through four points in the tropical projective plane and a counterexample to the incidence version of Pappus' Theorem.

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