English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

Let $X$ be a normal projective variety over a complete discretely valuedfield and $L$ a line bundle on $X$. We denote by $X^\textrm{an}$ theanalytification of $X$ in the sense of Berkovich and equip the analytification$L^\textrm{an}$ of $L$ with a continuous metric $\| \ \|$. We studynon-archimedean volumes, a tool which allows us to control the asymptoticgrowth of small sections of big powers of $L$. We prove that thenon-archimedean volume is differentiable at a continuous semipositive metricand that the derivative is given by integration with respect to aMonge-Amp\`ere measure. Such a differentiability formula had been proposed byM. Kontsevich and Y. Tschinkel. In residue characteristic zero, it implies anorthogonality property for non-archimedean plurisubharmonic functions whichallows us to drop an algebraicity assumption in a theorem of S. Boucksom, C.Favre and M. Jonsson about the solution to the non-archimedean Monge-Amp\`{e}reequation. The appendix by R. Lazarsfeld establishes the holomorphic Morseinequalities in arbitrary characteristic.

Differentiability of non-archimedean volumes and non-archimedean Monge-Amp\`ere equations (with an appendix by Robert Lazarsfeld)