Geodesic
The existence of a~smooth divisor on Fano 4-folds of index~2
Sbornik. Mathematics, Tome 83 (1995) no. 1, pp. 119-131

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Let $X$ be a smooth Fano 4-fold of index 2, and $H$ a fundamental divisor on $X$, that is, an ample divisor such that $K_X=2H$. It is proved that there is a smooth irreducible element in the linear system $|H|$. 
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     author = {Yu. G. Prokhorov},
     title = {The existence of a~smooth divisor on {Fano} 4-folds of index~2},
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Yu. G. Prokhorov. The existence of a~smooth divisor on Fano 4-folds of index~2. Sbornik. Mathematics, Tome 83 (1995) no. 1, pp. 119-131. http://geodesic.mathdoc.fr/item/SM_1995_83_1_a5/