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2007-19

Notes on the roots of steiner polynomials

by Henk, M., Hernández Cifre, M. A..


Series: 2007-19, Preprints

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

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