Notes on the roots of Steiner polynomials
Metric Geometry
2007-05-23 v1
Abstract
We study the location and the size of the roots of Steiner polynomials of convex bodies in the Minkowski relative geometry. Based on a problem of Teissier on the intersection numbers of Cartier divisors of compact algebraic varieties it was conjectured that these roots have certain geometric properties related to the in- and circumradius of the convex body. We show that the roots of 1-tangential bodies fulfill the conjecture, but we also present convex bodies violating each of the conjectured properties.
Keywords
Cite
@article{arxiv.math/0703373,
title = {Notes on the roots of Steiner polynomials},
author = {Martin Henk and María A. Hernández Cifre},
journal= {arXiv preprint arXiv:math/0703373},
year = {2007}
}