Scientific article

Polynomial systems with few real zeroes

Published inMathematische Zeitschrift, vol. 253, no. 2, p. 361-385
Publication date2006

We study some systems of polynomials whose support lies in the convex hull of a circuit, giving a sharp upper bound for their numbers of real solutions. This upper bound is non-trivial in that it is smaller than either the Kouchnirenko or the Khovanskii bounds for these systems. When the support is exactly a circuit whose affine span is Zn, this bound is 2n +1, while the Khovanskii bound is exponential in n2. The bound 2n + 1 can be attained only for non-degenerate circuits. Our methods involve a mixture of combinatorics, geometry, and arithmetic.

Citation (ISO format)
BERTRAND, Benoît, BIHAN, Frédéric, SOTTILE, Frank. Polynomial systems with few real zeroes. In: Mathematische Zeitschrift, 2006, vol. 253, n° 2, p. 361–385. doi: 10.1007/s00209-005-0912-8
Main files (1)
Article (Published version)
ISSN of the journal1432-1823

Technical informations

Creation10/15/2010 10:46:00 AM
First validation10/15/2010 10:46:00 AM
Update time03/14/2023 4:07:33 PM
Status update03/14/2023 4:07:33 PM
Last indexation01/15/2024 9:42:49 PM
All rights reserved by Archive ouverte UNIGE and the University of GenevaunigeBlack