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Mathematics > Metric Geometry

arXiv:math/0703373 (math)
[Submitted on 13 Mar 2007]

Title:Notes on the roots of Steiner polynomials

Authors: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.
Subjects: Metric Geometry (math.MG)
MSC classes: 52A20 (Primary); 52A39, 30C15 (Secondary)
Cite as: arXiv:math/0703373 [math.MG]
  (or arXiv:math/0703373v1 [math.MG] for this version)
  https://doi.org/10.48550/arXiv.math/0703373

Submission history

From: Martin Henk [view email]
[v1] Tue, 13 Mar 2007 10:59:22 UTC (78 KB)
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