English

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}
}
R2 v1 2026-07-22T17:52:35.015Z