Zurück zu den Preprints des Jahres 2007


Notes on the roots of steiner polynomials

by Henk, M., Hernández Cifre, M. A..

Series: 2007-19, Preprints

52A20 Convex sets in $n$ dimensions (including convex hypersurfaces)
52A39 Mixed volumes and related topics

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.

Steiner polynomial, Teissier's problem, tangential bodies, circumradius, inradius