On the /Lojasiewicz exponent at infinity of real polynomials
Volume 94 / 2008
Annales Polonici Mathematici 94 (2008), 197-208
MSC: Primary 14P10.
DOI: 10.4064/ap94-3-1
Abstract
Let $f \colon {\Bbb R}^n \rightarrow {\Bbb R}$ be a nonconstant polynomial function. Using the information from the “curve of tangency” of $f,$ we provide a method to determine the Łojasiewicz exponent at infinity of $f.$ As a corollary, we give a computational criterion to decide if the /Lojasiewicz exponent at infinity is finite or not. Then we obtain a formula to calculate the set of points at which the polynomial $f$ is not proper. Moreover, a relation between the /Lojasiewicz exponent at infinity of $f$ and the problem of computing the global optimum of $f$ is also established.
