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Complex geometry is the study of complex manifolds, complex algebraic varieties, complex analytic spaces, and, by extension, of almost complex structures. It is a part of differential geometry, algebraic geometry and analytic geometry.
8
votes
A geometric characterization for arithmetic genus
It is not true that quantities like the Todd genus (or the arithmetic genus) depend only on the underlying smooth manifold. There are examples of diffeomorphic Kaehler manifolds with different Todd ge …