Tropical Algebraic Geometry
نویسنده
چکیده
There are many examples in algebraic geometry in which complicated geometric or algebraic problems can be transformed into purely combinatorial problems. The most prominent example is probably given by toric varieties — a certain class of varieties that can be described purely by combinatorial data, e.g. by giving a convex polytope in an integral lattice. As a consequence, most questions about these varieties can be transformed into combinatorial questions on the defining polytope that are then hopefully easier to solve.
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PhD project offering: tropical scheme theory
Tropical geometry has burgeoned in the decade and a half since its coalescence as a field of study. It is a combinatorialization of algebraic geometry, associating to each algebraic variety a so-called tropical variety, a polyhedral complex that is its combinatorial “shadow”. In the simplest cases tropical geometry can be seen as the algebraic geometry over the tropical semiring T = (R ∪ {∞}, m...
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