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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.
M. Montserrat Alonso Ferrero. "On the index of contact." Annales Polonici Mathematici 83.1 (2004): 77-86. <http://eudml.org/doc/280732>.
@article{M2004, abstract = {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.}, author = {M. Montserrat Alonso Ferrero}, journal = {Annales Polonici Mathematici}, keywords = {multiplicity of proper and improper intersection; index and multiplicity of contact; Lojasiewicz exponent}, language = {eng}, number = {1}, pages = {77-86}, title = {On the index of contact}, url = {http://eudml.org/doc/280732}, volume = {83}, year = {2004}, }
TY - JOUR AU - M. Montserrat Alonso Ferrero TI - On the index of contact JO - Annales Polonici Mathematici PY - 2004 VL - 83 IS - 1 SP - 77 EP - 86 AB - 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. LA - eng KW - multiplicity of proper and improper intersection; index and multiplicity of contact; Lojasiewicz exponent UR - http://eudml.org/doc/280732 ER -