sentences:  A property of an irreducible algebraic variety "X" is said to be true generically if it holds except on a proper Zariski-closed subset of "X", in other words, if it holds on a non-empty Zariski-open subset.This definition agrees with the topological one above, because for irreducible algebraic varieties any non-empty open set is dense.For example, by the Jacobian criterion for regularity, a generic point of a variety over a field of characteristic zero is smooth.