Tropical Geometry
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High Quality Content by WIKIPEDIA articles! Tropical geometry is a relatively new area in mathematics, which might loosely be described as a piece-wise linear or skeletonized version of algebraic geometry. Its leading ideas had appeared in different guises in previous works of Bergman and of Bieri and Groves, but only since the late nineties has an effort been made to consolidate the basic definitions of the theory. This effort has been in great part motivated by the strong applications to enumerative algebraic geometry uncovered by Grigory Mikhalkin. Because it is such a recent and evolving…mehr

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High Quality Content by WIKIPEDIA articles! Tropical geometry is a relatively new area in mathematics, which might loosely be described as a piece-wise linear or skeletonized version of algebraic geometry. Its leading ideas had appeared in different guises in previous works of Bergman and of Bieri and Groves, but only since the late nineties has an effort been made to consolidate the basic definitions of the theory. This effort has been in great part motivated by the strong applications to enumerative algebraic geometry uncovered by Grigory Mikhalkin. Because it is such a recent and evolving area of research, there is not a standard formulation for the theory: some definitions are not universally accepted, and some basic results lack proofs.