Resumen de Invariants of singularities of pairs

Lawrence Ein, Mircea Mustat¡a

• 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.