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.Comment: 27 pages, minor changes according to the referees' comment

Ambro, Florin