Chern numbers and diffeomorphism types of projective varieties
D. Kotschick
TL;DR
This paper investigates which linear combinations of Chern numbers serve as topological invariants for smooth complex projective varieties, providing complete answers in low dimensions and partial results in general.
Contribution
It offers a comprehensive classification of topological invariants derived from Chern numbers in small dimensions and extends understanding to higher dimensions.
Findings
Complete characterization of Chern number invariants in small dimensions
Partial results on topological invariants in higher dimensions
Answer to Hirzebruch's 1954 question in specific cases
Abstract
In 1954 Hirzebruch asked which linear combinations of Chern numbers are topological invariants of smooth complex projective varieties. We give a complete answer to this question in small dimensions, and also prove partial results without restrictions on the dimension.
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