Monodromy of a family of hypersurfaces

Let $Y$ be an $(m+1)$-dimensional irreducible smooth complex projective variety embedded in a projective space. Let $Z$ be a closed subscheme of $Y$, and $delta$ be a positive integer such that $mathcal I_{Z,Y}(delta)$ is generated by global sections. Fix an integer $dgeq delta +1$, and assume the general divisor $X in |H^0(Y,ic_{Z,Y}(d))|$ is smooth. Denote by $H^m(X;mathbb Q)_{perp Z}^{text{van}}$ the quotient of $H^m(X;mathbb Q)$ by the cohomology of $Y$ and also by the cycle classes of the irreducible components of dimension $m$ of $Z$. In the present paper we prove that the monodromy representation on $H^m(X;mathbb Q)_{perp Z}^{text{van}}$ for the family of smooth divisors $X in |H^0(Y,ic_{Z,Y}(d))|$ is irreducible.