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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