Counting solutions of polynomial systems via iterated fibrations

. The paper introduces a new polynomial to count the solutions of a system of polynomial equations and inequations over an algebraically closed field of characteristic zero based on the triangular decomposition algorithm by J. M. Thomas of the nineteen-thirties. In the special case of projective var...

Full description

Saved in:
Bibliographic Details
Published inArchiv der Mathematik Vol. 92; no. 1; pp. 44 - 56
Main Author Plesken, Wilhelm
Format Journal Article
LanguageEnglish
Published Basel Birkhäuser-Verlag 2009
Subjects
Mathematics
Mathematics and Statistics
simple systems
solutions of polynomial systems
counting polynomial
Secondary 12Y05, 13P99, 14Q99
Primary 14N10, 14D06
Polynomial equations
polynomial inequations
Thomas algorithm
triangular decomposition
Online AccessGet full text

Cover

More Information
Summary:. The paper introduces a new polynomial to count the solutions of a system of polynomial equations and inequations over an algebraically closed field of characteristic zero based on the triangular decomposition algorithm by J. M. Thomas of the nineteen-thirties. In the special case of projective varieties examples indicate that it is a finer invariant than the Hilbert polynomial.
ISSN:0003-889X
1420-8938
DOI:10.1007/s00013-008-2785-7