complex geometry

The geometry of Kähler varieties: complex and metric

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Kählerian varieties establish themselves as an essential pillar of modern geometry, uniquely combining complex, metric, and symplectic structures. Their applications transcend mathematical boundaries, fueling advances in topology, theoretical physics, and complex algebraic geometry. Each instance of a Kählerian variety illustrates a subtle balance between geometric rigidity and analytical flexibility, conditioned by profound properties such as … Read more

Riemann surfaces: complex geometry and topology

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Riemann surfaces represent an essential pillar in the advanced study of complex functions, subtly merging complex geometry and topology. Their two-dimensional structure, often compared to shapes with holes or edges, serves to explore deep mathematical areas such as holomorphic functions, complex varieties, and Riemannian metrics. Through these surfaces, mathematicians can decipher the complex behaviors of … Read more