One-nodal Fano threefolds with Picard number one

Abstract

We classify all 1-nodal degenerations of smooth Fano threefolds with Picard number 1 (both nonfactorial and factorial) and describe their geometry. In particular, we describe a relation between such degenerations and smooth Fano threefolds of higher Picard rank and with unprojections of complete intersection varieties.

79 pages; v2: 1-cuspidal factorial Fano threefolds included into the classification; 83 pages