English

Dequantization of real algebraic geometry on logarithmic paper

Algebraic Geometry 2007-05-23 v3

Abstract

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.

Keywords

Cite

@article{arxiv.math/0005163,
  title  = {Dequantization of real algebraic geometry on logarithmic paper},
  author = {Oleg Viro},
  journal= {arXiv preprint arXiv:math/0005163},
  year   = {2007}
}

Comments

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 correct consequences of a miscalculation, a reference updated

R2 v1 2026-07-22T16:32:44.574Z