Successive minima of line bundles

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

A travel guide to the canonical bundle formula

We survey known results on the canonical bundle formula and its applications in algebraic geometry.Comment: 17 pages, to appear in the Proceedings of the conference Birational Geometry and Moduli Space