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, which is a non-negative integer counting the quantity of holes during the presented compact Riemann surface area.

complex variables. To define a projective complex algebraic wide range, a person involves the subset X ⊆ C P n displaystyle Xsubseteq mathbb CP ^ n

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Samples of vanishing theorems in complex geometry consist of the Kodaira vanishing theorem for the cohomology of line bundles on compact Kähler manifolds, and Cartan's theorems A and B for the cohomology of coherent sheaves on affine complex varieties.

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Complex geometry is worried about the review of complex manifolds, and complex algebraic and complex analytic versions. On this area, most of these Areas are defined as well as interactions among them offered.

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