Characteristic classes of symmetric products of complex quasi-projective varieties

Details Characteristic classes of symmetric products of complex quasi-projective varieties Characteristic classes of symmetric products of complex quasi-projective varieties

2010-08-25

arxiv.org/abs/1008.4299v2

Mathematics

Algebraic Geometry

Reference to the joint paper with M. Saito about symmetric products of mixed Hodge modules (arXiv:1008.5345) updated

Scientific paper

We prove a generating series formula for the characteristic classes of symmetric powers of complexes of mixed Hodge modules on the corresponding symmetric products of a complex quasi-projective variety. As a special case, we obtain a generating series formula for the Brasselet-Schuermann-Yokura (intersection) homology Hirzebruch classes of symmetric products. Moreover, after a suitable re-normalization procedure, we recover as a corollary Ohmoto's generating series formula for the rationalized MacPherson homology Chern classes of symmetric products.

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