Journal Article10.1090/cbms/097/09
Tropical algebraic geometry
Keyvan Yaghmayi,Tommaso de Fernex +1 more
- 12 Sep 2002
pp 119-131
TL;DR: Tropical algebraic geometry is the study of algebraic geometry over the tropical semifield, where the tropical sum is maximum and the tropical product is the usual addition.
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Abstract: The most straightforward way to tropical algebraic geometry is doing algebraic geometry on tropical semifield where the tropical sum is maximum and the tropical product is the usual addition: . Ideally, one may hope that every construction in algebraic geometry should have a tropical counterpart and thus, obtain results in algebraic geometry by looking at the tropical picture and then trying to transfer the results back to the original setting. We can look at as the Maslov dequantization of the semifield . Let for . The bijection given by induces a semifield structure on such that is an isomorphism. So, is a semifield and for we have:
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