Relating Catlin and D'Angelo q-types

We clarify the relationship between the two most standard measurements of the order of contact of q-dimensional complex varieties with a real hypersurface, the Catlin and D'Angelo $q$-types, by showing that the former equals the generic value of the normalized order of contact measured along curves whose infimum is by definition the D'Angelo $q$-type.
15 pages; new results added and more details in the proof of the Main Theorem. arXiv admin note: text overlap with arXiv:1302.2294