Dequantization of real algebraic geometry on logarithmic paper

Details Dequantization of real algebraic geometry on logarithmic paper Dequantization of real algebraic geometry on logarithmic paper

2000-05-16

arxiv.org/abs/math/0005163v3

Mathematics

Algebraic Geometry

12 pages, 3 figures, Plenary talk at the 3rd ECM, Barcelona, July 10-14, 2000. Sections 2.2, 3.3, 3.4 changed, 2.3 removed to

Scientific paper

On logarithmic paper some real algebraic curves look like smoothed broken lines. Moreover, the broken lines can be obtained as limits of those curves. The corresponding deformation can be viewed as a quantization, in which the broken line is a classical object and the curves are quantum. This generalizes to a new connection between algebraic geometry and the geometry of polyhedra, which is more straight-forward than the other known connections and gives a new insight into constructions used in the topology of real algebraic varieties.

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