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Let X be a smooth complex projective variety and let L be a line bundle on it. We describe the structure of the pre-polarized manifold (X,L) for non integral values of the invariantL(R) := KX · /(L · ), where is a minimal curve of an extremal ray R := R+() on X such that L · R > 0.

EXTREMAL RAYS OF NON-INTEGRAL L-LENGTH