Notes on the roots of Steiner polynomials

Details Notes on the roots of Steiner polynomials Notes on the roots of Steiner polynomials

2007-03-13

arxiv.org/abs/math/0703373v1

Mathematics

Metric Geometry

Scientific paper

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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