We use the construction of the intersection product of two algebraic cones to prove that the multiplicity of contact of the cones at the vertex is equal to the product of their degrees. We give an example to show that in order to calculate the index of contact it is not sufficient to perform the analytic intersection algorithm with hyperplanes.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap83-1-9,
author = {M. Montserrat Alonso Ferrero},
title = {On the index of contact},
journal = {Annales Polonici Mathematici},
volume = {83},
year = {2004},
pages = {77-86},
zbl = {1066.32011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap83-1-9}
}
M. Montserrat Alonso Ferrero. On the index of contact. Annales Polonici Mathematici, Tome 83 (2004) pp. 77-86. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap83-1-9/