Successive minima of line bundles

Ambro, Florin; Ito, Atsushi

doi:10.1016/j.aim.2020.107045

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Successive minima of line bundles

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Ambro, Florin
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1016/j.aim.2020.107045
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arXiv:1901.09341.pdf
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Citation

Ambro, F., & Ito, A. (2020). Successive minima of line bundles. Advances in Mathematics, 365: 107045. doi:10.1016/j.aim.2020.107045.

Cite as: https://hdl.handle.net/21.11116/0000-0006-9973-C

Abstract

We introduce and study the successive minima of line bundles on proper
algebraic varieties. The first (resp. last) minima are the width (resp.
Seshadri constant) of the line bundle at very general points. The volume of the
line bundle is equivalent to the product of the successive minima. For line
bundles on toric varieties, the successive minima are equivalent to the
(reciprocal of) usual successive minima of the difference of the moment
polytope.