Calabi–Yau threefolds with small h 1,1 's from Fano threefolds

We construct Calabi–Yau threefolds with relatively small Hodge numbers h 1 , 1 's by smoothing normal crossing varieties, which are obtained from Fano threefolds. We consider over 300 configurations and compute Hodge numbers of Calabi–Yau threefolds. Many of those Hodge pairs ( h 1 , 1 , h 1 , 2 ) do not overlap with those of Calabi–Yau threefolds constructed in the toric setting.