Stringy Chern classes of singular varieties

Authors:
  • TFTommaso de Fernex
    Tommaso de Fernex
  • ELErnesto Lupercio
    Ernesto Lupercio
  • TNThomas Nevins
    Thomas Nevins
  • BUBernardo Uribe
    Bernardo Uribe
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Abstract
Motivic integration and MacPherson's transformation are combined in this paper to construct a theory of "stringy" Chern classes for singular varieties. These classes enjoy strong birational invariance properties, and their definition encodes data coming from resolution of singularities. The singularities allowed in the theory are those typical of the minimal model program; examples are given by quotients of manifolds by finite groups. For the latter an explicit formula is proven, assuming that the canonical line bundle of the manifold descends to the quotient. This gives an expression of the stringy Chern class of the quotient in terms of Chern-Schwartz-MacPherson classes of the fixed-point set data.