Proposition 20.1.43AEC81016D4BC

Proposition 20.1.43.AEC81016D4BC

1. 413103745994

   The product in definition 20.1.41 is symmetric in its $n$ variables.

2. E21CF2D200CF

   Let $\mathbb {D}_1,\ldots ,\mathbb {D}_ n,\mathbb {D}'_1$ be nef b-divisors over $X$. Then

   \[ \left(\mathbb {D}_1+\mathbb {D}_1',\ldots ,\mathbb {D}_ n \right)=\left(\mathbb {D}_1,\ldots ,\mathbb {D}_ n \right)+\left(\mathbb {D}_1',\ldots ,\mathbb {D}_ n \right). \]
3. F1CD812A96DA

   Let $\mathbb {D}_1,\ldots ,\mathbb {D}_ n$ be nef b-divisors over $X$ and $\lambda \geq 0$. Then

   \[ \left(\lambda \mathbb {D}_1,\ldots ,\mathbb {D}_ n \right)=\lambda \left(\mathbb {D}_1,\ldots ,\mathbb {D}_ n \right). \]
4. B5FA9D24DE24

   Let $\mathbb {D}_1,\ldots ,\mathbb {D}_ n$ and $\mathbb {D}'$ be nef b-divisors over $X$ such that $\mathbb {D}_1\leq \mathbb {D}'$. Then

   \[ \left(\mathbb {D}_1,\ldots ,\mathbb {D}_ n \right)\leq \left(\mathbb {D}',\mathbb {D}_2,\ldots ,\mathbb {D}_ n \right). \]
5. 2960B6AF1379

   Let $T_1,\ldots ,T_ n$ be closed positive $(1,1)$-currents on $X$. Then

   \[ \Bigl ( \mathbb {D}(T_1),\ldots ,\mathbb {D}(T_ n) \Bigr )= \operatorname{vol}(T_1,\ldots ,T_ n). \]