The Variation of Singular Cycles in an Algebraic Family of Morphisms

(1) Let <!-- MATH $g:{V^r} \to {W^m}(m \geqq r)$ --> be a morphism of nonsingular varieties over an algebraically closed field. Under certain conditions, one can define a cycle on with <!-- MATH $\operatorname{Supp} ({S_i}) = \{ x|{\dim _{k(x)}}(\Omega _{X/Y}^1)(x) \geqq i\}$ --> .