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Notes on the roots of Steiner polynomials

Martin Henk·María A. Hernández Cifre
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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.

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Martin Henk, María A. Hernández Cifre. 2007-03-13. Notes on the roots of Steiner polynomials. https://arxiv.org/abs/math/0703373

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