Topologically invariant Chern numbers of projective varieties

Details Topologically invariant Chern numbers of projective varieties Topologically invariant Chern numbers of projective varieties

2009-03-09

arxiv.org/abs/0903.1587v2

Advances in Mathematics 229 (2012), pp. 1300-1312

Mathematics

Geometric Topology

11 pages; minor edits in final version, to appear in Adv. Math

Scientific paper

10.1016/j.aim.2011.10.020

We prove that a rational linear combination of Chern numbers is an oriented diffeomorphism invariant of smooth complex projective varieties if and only if it is a linear combination of the Euler and Pontryagin numbers. In dimension at least three we prove that only multiples of the top Chern number, which is the Euler characteristic, are invariant under diffeomorphisms that are not necessarily orientation-preserving. These results solve a long-standing problem of Hirzebruch's. We also determine the linear combinations of Chern numbers that can be bounded in terms of Betti numbers.

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