I am looking for a reference to the following fact: monodromy group acting on the cohomology of smooth hyperplane sections of a smooth projective variety $X$ over $\mathbb C$ is preserved under isomorphic projection.

To be precise, suppose that $X\subset \mathbb P^N$ is a smooth projective variety of dimension $n+1$ and $Y$ is its smooth hyperplane section. As $Y$ varies in the class of smooth hyperplane sections of $X$, a monodromy action on $H^n(Y,\mathbb Z)$ arises; by monodromy group of $X$ I will mean the corresponding subgroup of $\mathrm{Aut}(H^n(Y,\mathbb Z))$.

Suppose now that there exists a pont $p\in\mathbb P^N\setminus Y$ such that the projection $\pi_p\colon X\to X'\subset\mathbb P^{N-1}$ is an isomorphism. Do you know a reference to the effect that this monodromy group of $X'$ is the same as that of $X$?

Thank you in avance,
Serge

I am looking for a reference to the following fact: monodromy group acting on the cohomology of smooth hyperplane sections of a smooth projective variety $X$ over $\mathbb C$ is preserved under isomorphic projection.

To be precise, suppose that $X\subset \mathbb P^N$ is a smooth projective variety of dimension $n+1$ and $Y$ is its smooth hyperplane section. As $Y$ varies in the class of smooth hyperplane sections of $X$, a monodromy action on $H^n(Y,\mathbb Z)$ arises; by monodromy group of $X$ I will mean the corresponding subgroup of $\mathrm{Aut}(H^n(Y,\mathbb Z))$.

Suppose now that there exists a pont $p\in\mathbb P^N\setminus Y$ such that the projection $\pi_p\colon X\to X'\subset\mathbb P^{N-1}$ is an isomorphism. Do you know a reference to the effect that this monodromy group of $X'$ is the same as that of $X$?

Thank you in advance,
Serge