Polynomial systems supported on circuits and dessins d'enfants

Details Polynomial systems supported on circuits and dessins d'enfants Polynomial systems supported on circuits and dessins d'enfants

2005-09-09

arxiv.org/abs/math/0509219v2

Mathematics

Algebraic Geometry

19 pages, 5 figures, Section 3.1 revised, minor changes in other sections

Scientific paper

We study polynomial systems whose equations have as common support a set C of n+2 points in Z^n called a circuit. We find a bound on the number of real solutions to such systems which depends on n, the dimension of the affine span of the minimal affinely dependent subset of C, and the "rank modulo 2" of C. 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 systems supported on circuits in Z^n is n+1, which is very small comparatively to the bound given by the Khovanskii fewnomial theorem.

Affiliated with

Also associated with

No associations

Rating

Polynomial systems supported on circuits and dessins d'enfants does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Polynomial systems supported on circuits and dessins d'enfants, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Polynomial systems supported on circuits and dessins d'enfants will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-464739