Calabi–Yau threefolds with small h1,1's from Fano threefolds

Abstract

We construct Calabi–Yau threefolds with relatively small Hodge numbers h1,1'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 (h1,1,h1,2) do not overlap with those of Calabi–Yau threefolds constructed in the toric setting.