TY - JOUR
T1 - Generating functions of orbifold Chern classes I
T2 - Symmetric products
AU - Ohmoto, Toru
N1 - Funding Information:
Acknowledgements. The author would like to thank Jörg Schürmann, Shoji Yokura and also the referee for useful comments. This work is partially supported by Grant-in-Aid for Scientific Research (No.17340013), JSPS.
PY - 2008/3
Y1 - 2008/3
N2 - In this paper, for a possibly singular complex variety X, generating functions of total orbifold Chern homology classes of the symmetric products SnX are given. These are very natural class versions of known generating function formulae of (generalized) orbifold Euler characteristics of SnX. Our Chern classes work covariantly for proper morphisms. We state the result more generally. Let G be a finite group and Gn the wreath product G Sn. For a G-variety X and a group A, we show a DeyWohlfahrt type formula for equivariant ChernSchwartzMacPherson classes associated to Gn-representations of A (Theorem 11 and 12). When X is a point, our formula is just the classical one in group theory generating numbers |Hom(A, Gn)|.
AB - In this paper, for a possibly singular complex variety X, generating functions of total orbifold Chern homology classes of the symmetric products SnX are given. These are very natural class versions of known generating function formulae of (generalized) orbifold Euler characteristics of SnX. Our Chern classes work covariantly for proper morphisms. We state the result more generally. Let G be a finite group and Gn the wreath product G Sn. For a G-variety X and a group A, we show a DeyWohlfahrt type formula for equivariant ChernSchwartzMacPherson classes associated to Gn-representations of A (Theorem 11 and 12). When X is a point, our formula is just the classical one in group theory generating numbers |Hom(A, Gn)|.
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U2 - 10.1017/S0305004107000898
DO - 10.1017/S0305004107000898
M3 - Article
AN - SCOPUS:41549163212
VL - 144
SP - 423
EP - 438
JO - Mathematical Proceedings of the Cambridge Philosophical Society
JF - Mathematical Proceedings of the Cambridge Philosophical Society
SN - 0305-0041
IS - 2
ER -