Real Algebraic and Analytic Geometry |

Polynomial systems supported on circuits and dessins d'enfants.

e-mail:

Submission: 2005, September 20.

*Abstract:
We study real solutions to polynomial systems whose equations
have as common support a set, called a circuit, of n+2 points in Z^n.
We find a bound on the number of real
solutions to such systems which depends on n and two characteristic numbers of
the circuit. We prove that this bound is sharp
by drawing so-called dessins d'enfant on the Riemann sphere.
We also obtain that the maximal number of solutions
with positive coordinates to such systems is n+1, which
is very small comparatively to the bound given by the Khovanskii fewnomial
theorem.*

Mathematics Subject Classification (2000): 12D10, 14M25.

Keywords and Phrases: polynomial systems, real solutions, Fewnomials.

**Full text**, 19p.:
pdf 260k.

Server Home Page