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.
@article{1218475357,
author = {Henk
,
Martin and Hern\'andez Cifre
,
Mar\'\i a A.},
title = {Notes on the roots of Steiner polynomials},
journal = {Rev. Mat. Iberoamericana},
volume = {24},
number = {2},
year = {2008},
pages = { 631-644},
language = {en},
url = {http://dml.mathdoc.fr/item/1218475357}
}
Henk
,
Martin; Hernández Cifre
,
María A. Notes on the roots of Steiner polynomials. Rev. Mat. Iberoamericana, Tome 24 (2008) no. 2, pp. 631-644. http://gdmltest.u-ga.fr/item/1218475357/