Definition 13.9.14F64B29C315E

Definition 13.9.1.4F64B29C315E For big classes $\alpha _ j=\{ \theta _ j\} $, $1\leq j\leq p\leq n$, the positive mixed intersection number relative to the Kähler class $\{ \omega \} $ is

For pseudo-effective classes $\alpha _ j$ that are not all big, we define $I_\omega (\alpha _1,\ldots ,\alpha _ p)$ as the limit of the numbers $I_\omega (\alpha _1+\varepsilon \{ \omega \} ,\ldots ,\alpha _ p+\varepsilon \{ \omega \} )$, which decrease as $\varepsilon \downarrow 0$ (proposition 13.9.2); when all $\alpha _ j$ are big, the same limit equals the number defined by the display. In top degree we put $\operatorname {vol}(\alpha )=I_\omega (\alpha ,\ldots ,\alpha )$, the volume of $\alpha $; the factor $\omega ^{n-p}$ is then absent.