We present exponential formulas for the number of hypersurfaces in a k-dimensional family displaying k ordinary double points for k<7.
Example: how many cubic surfaces pass through 19-4 points in P3 and display 4 distinct, ordinary double points? (Maria J. Vazquez from Spain wrote a thesis on things of this sort; unfortunately she missed "corrections" due to co-rank 2 singularities. She was misled by the case of curves, where corrections came essentially from triple points; believing the analogy for higher dimension would be ipsis literi, hence not present at all due to a naive count of constants, ergo, corrections not needed.)
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