Towards connectivity for codimension 2 cycles: Infinitesimal deformations

Let X be a smooth projective variety over an algebraically closed field k⊂C of characteristic zero, and Y⊂X a smooth complete intersection. The Weak Lefschetz Theorem states that the natural restriction map Hi(X(C),Q)→Hi(Y(C),Q) on singular cohomology is an isomorphism for all i