Topology versus Chern Numbers for Complex 3-Folds

1998/01/29 by Claude LeBrun, LeBrun, Claude
Mathematics · #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #math.AG #math.DG

paper · pdf · doi:10.48550/arxiv.math/9801133

8 pages, LaTeX2e

arxiv created 1998/01/29 · arxiv updated 2009/11/30

Abstract

We show by example that the Chern numbers c₁³ and c₁ c₂ of a complex 3-fold are not determined by the topology of the underlying smooth compact 6-manifold. In fact, we observe that infinitely many different values of a Chern number can be achieved by (integrable) complex structures on a fixed 6-manifold.

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