Final Report Summary - TROPGEO (Tropical Geometry)
The project developed Tropical Geometry. This is a regime of geometry where the arguments (phases) of the coordinates may be ignored while the absolute value is logarithmically rescaled (using a very large base). The resulting geometric objects become piecewise-linear. In particular, smooth curves become metric graphs. The project has advanced the theory of tropical curves, with a focus on enumerative geometry. Also, it has started to develop algebraic topology theories for tropical varieties and to systematically apply tropical tools in real algebraic geometry. A major finding of the project is tropical invariance of the so-called Block-Göttsche invariants (the quantization of curve's enumeration).