Let $X$ be a smooth projective variety over an algebraically closed field $k$. Let $NS(X)$ denote the group $[Pic(X)/Pic^a(X)]\otimes_{\mathbb{Z}}\mathbb{Q}$, where $Pic^a(X)$ denotes the divisors which are algebraically equivalent to 0. If $X$ is a surface, then the pairing on $NS(X)$ given by $(D,D')\mapsto D\cdot D'$ is non-degenerate.

For higher dimensions, let $\Theta$ denote an ample divisor on $X$. Let $d$ be the dimension of $X$. Is it true that the pairing on $NS(X)$ given by $(D,D')\mapsto D\cdot D'\cdot \Theta^{d-2}$ is non-degenerate.

Is there a good reference for the above result.

$\DeclareMathOperator\NS{NS}\DeclareMathOperator\Pic{Pic}$Let $X$ be a smooth projective variety over an algebraically closed field $k$. Let $\NS(X)$ denote the group $[\Pic(X)/\Pic^{\text a}(X)]\otimes_{\mathbb{Z}}\mathbb{Q}$, where $\Pic^{\text a}(X)$ denotes the divisors which are algebraically equivalent to 0. If $X$ is a surface, then the pairing on $\NS(X)$ given by $(D,D')\mapsto D\cdot D'$ is non-degenerate.

For higher dimensions, let $\Theta$ denote an ample divisor on $X$. Let $d$ be the dimension of $X$. Is it true that the pairing on $\NS(X)$ given by $(D,D')\mapsto D\cdot D'\cdot \Theta^{d-2}$ is non-degenerate?

Is there a good reference for the above result?