Chern classes of birational varieties

Details Chern classes of birational varieties Chern classes of birational varieties

2004-01-14

arxiv.org/abs/math/0401167v2

Int. Math. Res. Not. 2004, no. 63, 3367-3377

Mathematics

Algebraic Geometry

8 pages, final version, to appear in IMRN

Scientific paper

10.1155/S1073792804140439

A theorem of Batyrev's asserts that if two nonsingular varieties V,W are birational, and their canonical bundles agree after pull-back to a resolution of indeterminacies of a birational map between them, then the Betti numbers of V and W coincide. We prove that, in the same hypotheses, the total homology Chern classes of V and W are push-forwards of the same class in the Chow group of the resolution. For example, it follows that the push-forward of the total Chern class of a crepant resolution of a singular variety is independent of the resolution.

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