by Henk, M., Hernández Cifre, M. A..
Series: 2007-19, Preprints
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