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Nonvanishing of a plurigenus of a threefold of general type

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Abstract

When X is a threefold of general type, it is well knownh^0(X,cx(nK_X))geq 1 for a sufficiently large n. When ex>0, it is not easy to obtain such an integer n. A. R. Fletchershowed that h^0(X,cx(nK_X))geq 1 for n=12 when ex=1.We introduce a technique different from A. R. Fletcher's. Using this technique,we also prove the same result as he showed and have a new result.

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