A primer on Seshadri constants

Details A primer on Seshadri constants A primer on Seshadri constants

2008-10-04

arxiv.org/abs/0810.0728v2

Contemporary Mathematics 496 (2009), 33-70

Mathematics

Algebraic Geometry

37 pages, notes taken after the workshop on Seshadri consants held in Essen 12-15 Februar 2008, dedicated to Andrew J. Sommese

Scientific paper

Seshadri constants express the so called local positivity of a line bundle on a projective variety. They were introduced by Demailly. The original idea of using them towards a proof of the Fujita conjecture failed but they quickly became a subject of intensive study quite in their own right. Lazarsfeld's book "Positivity in Algebraic Geometry" contains a whole chapter devoted to local positivity and serves as a very enjoyable introduction to Seshadri constants. Since this book has appeared, the subject witnessed quite a bit of development. It is the aim of these notes to give an account of recent progress as well as to discuss many open questions and provide some examples.

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