Growth at infinity and index of polynomial maps

摘要

Let F : K-n --> K-n be a polynomial map such that F-1(0) is compact, where K = R or C. Then we give a condition implying that there is a uniform bound for the Lojasiewicz exponent at infinity in certain deformations of F. This fact gives a result about the invariance of the global index of F. (C) 2014 Elsevier Inc. All rights reserved.