Continuity of volumes on arithmetic varieties

DOI10.1090/S1056-3911-08-00500-6zbMath1167.14014arXivmath/0612269MaRDI QIDQ3632495

Atsushi Moriwaki

Publication date: 11 June 2009

Published in: Journal of Algebraic Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0612269

zbMATH Keywords

continuityArakelov geometryHodge index theoremarithmetic volume function

Mathematics Subject Classification ID

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

Related Items (22)

Adelic Cartier divisors with base conditions and the continuity of volumes ⋮ Mahler measures and logarithmic equidistribution ⋮ Effective bound of linear series on arithmetic surfaces ⋮ An arithmetic Hilbert–Samuel theorem for singular hermitian line bundles and cusp forms ⋮ Higher dimensional essential minima and equidistribution of cycles ⋮ Estimation of arithmetic linear series ⋮ Arithmetic Okounkov bodies and positivity of adelic Cartier divisors ⋮ Toward a geometric analogue of Dirichlet's unit theorem ⋮ Adelic Divisors on Arithmetic Varieties ⋮ Effective bounds of linear series on algebraic varieties and arithmetic varieties ⋮ Toward Dirichlet's unit theorem on arithmetic varieties ⋮ On isoperimetric inequality in Arakelov geometry ⋮ Numerical characterization of nef arithmetic divisors on arithmetic surfaces ⋮ Big line bundles over arithmetic varieties ⋮ Boundedness of the successive minima on arithmetic varieties ⋮ Introduction to arithmetic Hilbert-Samuel theorems ⋮ Okounkov bodies of filtered linear series ⋮ Arithmetic positivity on toric varieties ⋮ Explicit majorizations of geometric and arithmetic Hilbert-Samuel functions ⋮ Roth's theorem over arithmetic function fields ⋮ On volumes of arithmetic line bundles ⋮ The theta invariants and the volume function on arithmetic varieties

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