is ample). Fano versions are of appreciable interest in complex algebraic geometry, and especially birational geometry, in which they usually occur within the small design application. Fundamental samples of Fano versions are specified by projective space C P n displaystyle mathbb CP ^ n
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As an example, famous problems within the analysis of numerous complex variables preceding the introduction of modern definitions will be the Cousin problems, inquiring specifically when regional meromorphic information could possibly be glued to acquire a global meromorphic function. These old challenges is usually just solved following the introduction of sheaves and cohomology groups.
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Special samples of sheaves Employed in complex geometry involve holomorphic line bundles (as well as the divisors linked to them), holomorphic vector bundles, and coherent sheaves. Due to the fact sheaf cohomology actions obstructions in complex geometry, just one procedure that's applied would be to demonstrate vanishing theorems.
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