Abstract
Kishimoto raised the problem to classify all compactifications of contractible affine [Formula: see text]-folds into smooth Fano [Formula: see text]-folds with second Betti number two and classified such compactifications whose log canonical divisors are not nef. In this paper, we show that there are [Formula: see text] deformation equivalence classes of smooth Fano [Formula: see text]-folds which can admit structures of such compactifications whose log canonical divisors are trivial. We also construct an example of such compactifications with trivial log canonical divisors for each of all the 14 classes.
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