Proposition 3.11 . [05A9]

Original official author HTML, exact retained edition. Historical TeX conversion verdicts remain unchanged. Cited-edition alignment and mathematical self-containment are not assessed.

Complete original source context · Original author HTML

Proposition 3.11.

Let $X$ be a proper scheme over $K$ and $L$ a line bundle on $X$ . Let $\|\cdot\|_{1},\|\cdot\|_{2}$ be two piecewise linear metrics on $L^{\textup{an}}$ which are semipositive in $x\in X^{\textup{an}}$ . Then $\|\cdot\|:=\min(\|\cdot\|_{1},\|\cdot\|_{2})$ is semipositive in $x$ .