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Cousin problems

In mathematics, the Cousin problems are two questions in several complex variables, concerning the existence of meromorphic functions that are specified in terms of local data. They were introduced in special cases by Pierre Cousin in 1895. They are now posed, and solved, for any complex manifold M, in terms of conditions on M.

First Cousin problem, Second Cousin problem & Overview

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First Cousin problem

Second Cousin problem

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Cousin problems

Nodes31
Edges30
Triples0
Avg. degree1.94
Density0.064516
Components1

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Important terminology

cousin displaystyle problem sheaf meromorphic function holomorphic first terms second cohomology sequence mathbf manifold given complex always quotient exact solvable

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