Characteristic numbers of algebraic varieties

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 3, only multiples of the top Chern number, which is the Euler characteris...

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Bibliographic Details
Published in:Proceedings of the National Academy of Sciences - PNAS 2009-06, Vol.106 (25), p.10114-10115
Main Author: Kotschick, D
Format: Article
Language:English
Subjects:
Algebra
Differential topology
Eigenvalues
Eulers equations
Homeomorphism
Linear algebra
Mathematical manifolds
Mathematical rings
Mathematical theorems
Physical Sciences
Signatures
Topological theorems
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Summary: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 3, only multiples of the top Chern number, which is the Euler characteristic, are invariant under diffeomorphisms that are not necessarily orientation preserving. In the space of Chern numbers, there are 2 distinguished subspaces, one spanned by the Euler and Pontryagin numbers, and the other spanned by the Hirzebruch-Todd numbers. Their intersection is the span of the Euler number and the signature.
ISSN:0027-8424
1091-6490
DOI:10.1073/pnas.0903504106