Let X be a smooth complex projective variety of dimension 3 and let L be an ample line bundle on X. In this article, we give a characterization of (X, L) with g(X, L)=q(X) and h(0)(L)=2, where g(X, L) (resp. q(X)) denotes the sectional genus of (X, L) (resp. the irregularity of X).
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