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Let be an algebraic variety in and when is an integer then denotes all holomorphic functions on satisfying for all and some constant . We estimate the least integer such that every admits an extension from into by a polynomial , of degree at most. In particular is related to cohomology groups with coefficients in coherent analytic sheaves on . The existence of the finite integer is for example an easy consequence of Kodaira’s Vanishing Theorem.
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