Arithmetic Demailly Approximation Theorem

arXiv2208.13230MaRDI QIDQ6409057

Hang Yin, Binggang Qu

Publication date: 28 August 2022

Abstract: We generalize the Demailly approximation theorem from complex geometry to Arakelov geometry.As an application, let $X/mathbbQ$ be an integral projective variety and $overlineN$ be an adelic line bundle on $X$, we prove that $operatornameess(overlineN)geq0$ $Longrightarrow$ $overlineN$ pseudo-effective. This was proved in [Bal21], assuming $overlineN$ relatively semipositive. We show in the appendix that the above assertion is also true for adelic line bundles on quasi-projective varieties, under the framework of [YZ22].

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