Stringy Chern classes of singular varieties

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.

24 pages; v2: small remarks and one reference added; v3: reviewed esposition, with minor changes and corrections and slightly greater generality in section 5; all main results remain unchanged; to appear in Advances in Math

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• Stringy Hodge numbers of varieties with Gorenstein canonical singularities
• Topological Orbifold Models and Quantum Cohomology Rings
• An introduction to motivic integration
• Modification systems and integration in their Chow groups
• Hirzebruch classes and motivic Chern classes for singular spaces
• Hirzebruch classes and motivic Chern classes for singular (complex) algebraic varieties
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Cited by in corpus (5)

• Equivariant Chern classes of singular algebraic varieties with group actions
• Modification systems and integration in their Chow groups
• A survey of characteristic classes of singular spaces
• Celestial integration, stringy invariants, and Chern-Schwartz-MacPherson classes
• Generating Functions of Orbifold Chern Classes I : Symmetric Products