On the Lojasiewicz exponent of the gradient of a polynomial function

Details On the Lojasiewicz exponent of the gradient of a polynomial function On the Lojasiewicz exponent of the gradient of a polynomial function

1997-03-19

arxiv.org/abs/math/9703224v1

Mathematics

Complex Variables

Scientific paper

Let h = \sum h_{\alpha \beta} X^\alpha Y^\beta be a polynomial with complex coefficients. The Lojasiewicz exponent of the gradient of h at infinity is the upper bound of the set of all real \lambda such that |grad h(x, y)| >= c|(x,y)|^\lambda in a neighbourhood of infinity in C^2, for c > 0. We estimate this quantity in terms of the Newton diagram of h. The equality is obtained in the nondegenerate case.

Affiliated with

Also associated with

No associations

Rating

On the Lojasiewicz exponent of the gradient of a polynomial function does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the Lojasiewicz exponent of the gradient of a polynomial function, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Lojasiewicz exponent of the gradient of a polynomial function will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-360554