Open Access
July, 2008 Notes on the roots of Steiner polynomials
Martin Henk , María A. Hernández Cifre
Rev. Mat. Iberoamericana 24(2): 631-644 (July, 2008).


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.


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Martin Henk . María A. Hernández Cifre . "Notes on the roots of Steiner polynomials." Rev. Mat. Iberoamericana 24 (2) 631 - 644, July, 2008.


Published: July, 2008
First available in Project Euclid: 11 August 2008

zbMATH: 1158.52003
MathSciNet: MR2459207

Primary: 52A20 , 52A39
Secondary: 30C15

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

Rights: Copyright © 2008 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.24 • No. 2 • July, 2008
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