Overview

In the case where the norms are induced by metrics on the fibres of ${\mathcal L}$, we establish the functoriality of the sectional capacity under base change, pullbacks by finite surjective morphisms, and products. We study the continuity of $S Gamma(\overline{\mathcal L})$ under variation of the metric and line bundle, and we apply this to show that the notion of $v$-adic sets in $X(\mathbb C v)$ of capacity $0$ is well-defined. Finally, we show that sectional capacities for arbitrary norms can be well-approximated using objects of finite type.

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Robert Elsie is the West's leading specialist on Albanian literature. He works as a freelance interpreter, primarily Albanian and German, and is the author of numerous books and articles on various aspects of Albanian culture and affairs. He lives in Germany.

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