On the Sharpness of fewnomial bound and the number of components of a fewnomial hypersurface
| dc.creator | Bihan, Frederic | |
| dc.creator | Rojas, J. Maurice | |
| dc.creator | Sottile, Frank | |
| dc.date | 2007-01-24 | |
| dc.date | 2007-05-22 | |
| dc.date.accessioned | 2026-07-07T08:02:44Z | |
| dc.date.available | 2026-07-07T08:02:44Z | |
| dc.description | We show the existence of systems of n polynomial equations in n variables, with a total of n+k+1 distinct monomial terms, possessing [n/k+1]^k nondegenerate positive solutions. (Here, [x] is the integer part of a positive number x.) This shows that the recent upper bound of (e^2+3)/4 2^{\binom{k}{2}} n^k for the number of nondegenerate positive solutions is asymptotically sharp for fixed k and large n. We also adapt a method of Perrucci to show that there are fewer than (e^2+3)/4 2^{\binom{k}{2}} 2^n n^k connected components in a smooth hypersurface in the positive orthant of R^n defined by a polynomial with n+k+1 monomials. Our results hold for polynomials with real exponents. | |
| dc.description | 5 pages, proof of main theorem corrected | |
| dc.identifier | https://arxiv.org/abs/math/0701667 | |
| dc.identifier | http://arxiv.org/abs/math/0701667 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/129319 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Commutative Algebra | |
| dc.subject | 14P99 | |
| dc.title | On the Sharpness of fewnomial bound and the number of components of a fewnomial hypersurface | |
| dc.type | text |