TY - JOUR
T1 - Stringy Chern classes of singular varieties
AU - de Fernex, Tommaso
AU - Lupercio, Ernesto
AU - Nevins, Thomas
AU - Uribe, Bernardo
N1 - Funding Information:
✩ The first author was partially supported by the University of Michigan Rackham Research Grant and the MIUR of the Italian Government, National Research Project “Geometry on Algebraic Varieties” (Cofin 2002). The second author was partially supported by CONACYT. The third author was partially supported by an NSF Postdoctoral Fellowship at the University of Michigan. Research of the fourth author was partially carried out during his visit at the Max Planck Institut, Bonn. * Corresponding author. E-mail addresses: [email protected] (T. de Fernex), [email protected] (E. Lupercio), [email protected] (T. Nevins), [email protected] (B. Uribe). 1 Current address: Institute for Advanced Study, School of Mathematics, 1 Einstein Drive, Princeton, NJ 08540, USA.
PY - 2007/1/30
Y1 - 2007/1/30
N2 - 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.
AB - 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.
KW - Chern class
KW - Constructible function
KW - Deligne-Mumford stack
KW - Grothendieck ring
KW - Motivic integration
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U2 - 10.1016/j.aim.2006.03.005
DO - 10.1016/j.aim.2006.03.005
M3 - Article
AN - SCOPUS:33750623823
SN - 0001-8708
VL - 208
SP - 597
EP - 621
JO - Advances in Mathematics
JF - Advances in Mathematics
IS - 2
ER -