Notes on the roots of Steiner polynomials

  • Martin Henk

    Technische Universität Berlin, Germany
  • María A. Hernández Cifre

    Universidad de Murcia, Spain


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.

Cite this article

Martin Henk, María A. Hernández Cifre, Notes on the roots of Steiner polynomials. Rev. Mat. Iberoam. 24 (2008), no. 2, pp. 631–644

DOI 10.4171/RMI/550