Big arithmetic divisors on the projective spaces over \(\mathbb{Z}\)

DOI10.1215/21562261-1299882zbMath1228.14023arXiv1003.1782OpenAlexW2128152343MaRDI QIDQ640822

Atsushi Moriwaki

Publication date: 21 October 2011

Published in: Kyoto Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1003.1782

zbMATH Keywords

Zariski decompositionbig arithmetic divisorprojective space over \(\mathbb{Z}\)

Mathematics Subject Classification ID

Heights (11G50) Arithmetic varieties and schemes; Arakelov theory; heights (14G40)

Related Items (6)

Arithmetic linear series with base conditions ⋮ Toward Dirichlet's unit theorem on arithmetic varieties ⋮ Numerical characterization of nef arithmetic divisors on arithmetic surfaces ⋮ Arithmetic positivity on toric varieties ⋮ Adelic Cartier divisors with base conditions and the Bonnesen-Diskant-type inequalities ⋮ The theta invariants and the volume function on arithmetic varieties

Cites Work

• Estimation of arithmetic linear series
• On the zeta function associated with the singular Laplacian \(\Delta_{\overline{\mathcal O(m)}_{\infty}}\)
• Arithmetic Hilbert-Samuel theorem
• Zariski decompositions on arithmetic surfaces
• An arithmetic Riemann-Roch theorem
• Resolution of singularities of an algebraic variety over a field of characteristic zero. I
• Arithmetic Fujita approximation
• On volumes of arithmetic line bundles
• Okounkov bodies of filtered linear series
• Convex and Discrete Geometry
• Convex Functions on Convex Polytopes

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