Invariants of singularities of pairs

  • Lawrence Ein

    University of Illinois at Chicago, USA
  • Mircea Mustaţă

    University of Michigan, Ann Arbor, United States
Invariants of singularities of pairs cover

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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.