PomeDefinition 19.3.6.78704BB19535 Let $T$ be a closed positive $(1,1)$-current on $X$. We define the valuation of $T$ along $Y_{\bullet }$ as
\[ \nu _{Y_{\bullet }}(T)=\left(\nu _{Y_{\bullet }}(T)_1,\ldots ,\nu _{Y_{\bullet }}(T)_ n\right)\in \mathbb {R}_{\geq 0}^ n \]
by induction on $n$. When $n=0$, we define $\nu _{Y_{\bullet }}(T)$ as the unique point in $\mathbb {R}^0$. When $n\geq 1$, we define
\[ \nu _{Y_{\bullet }}(T)_1=\nu (T,Y_1); \]
Then for $i=2,\ldots ,n$, we define
\[ \nu _{Y_{\bullet }}(T)_ i=\nu _{Y_1\supseteq \cdots \supseteq Y_ n}\left(\operatorname{Tr}_{Y_1}(T-\nu (T,Y_1)[Y_1])\right)_{i-1}. \]
Comments
Corrections, questions, and mathematical discussion are welcome. Sign in with GitHub to comment. Comments are public.