Invariants of singularities of pairs

Details Invariants of singularities of pairs Invariants of singularities of pairs

2006-04-27

arxiv.org/abs/math/0604601v2

Mathematics

Algebraic Geometry

19 pages, to appear in Proceedings of the International Congress of Mathematicians, Madrid, Spain, 2006 (talk to be given by t

Scientific paper

Let X be a smooth complex variety and Y be a closed subvariety of X, or more generally, a closed subscheme of X. We are interested in invariants attached to the singularities of the pair (X, Y). We discuss various methods to construct such invariants, coming from the theory of multiplier ideals, D-modules, the geometry of the space of arcs and characteristic p techniques. We present several applications of these invariants to algebra, higher dimensional birational geometry and to singularities.

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