X-Nico

3 unusual facts about complex manifold


Complex manifold

A Calabi–Yau manifold can be defined as a compact Ricci-flat Kähler manifold or equivalently one whose first Chern class vanishes.

Riemann surfaces, two dimensional manifolds equipped with a complex structure, which are topologically classified by the genus, are an important example of this phenomenon.

Galactooligosaccharide

The gut and immune system form a complex structure that provides defence against ingested toxins and pathogenic bacteria.


Global section functor

Let \mathcal O X be the sheaf of holomorphic functions on the compact connected complex manifold X, then by the maximum principle, global sections are constant, ie. \Gamma (X, \mathcal O X) = \mathbb C


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