Stringy Chern classes of singular varieties

Tommaso de Fernex, Ernesto Lupercio, Thomas Nevins, Bernardo Uribe

Research output: Contribution to journalArticlepeer-review


Motivic integration [M. Kontsevich, Motivic integration, Lecture at Orsay, 1995] and MacPherson's transformation [R. MacPherson, Chern classes for singular varieties, Ann. of Math. 100 (1974) 423-432] 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.

Original languageEnglish (US)
Pages (from-to)597-621
Number of pages25
JournalAdvances in Mathematics
Issue number2
StatePublished - Jan 30 2007


  • Chern class
  • Constructible function
  • Deligne-Mumford stack
  • Grothendieck ring
  • Motivic integration

ASJC Scopus subject areas

  • General Mathematics


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