Congruences on G(1,4) with split universal quotient bundle

Abstract

This work provides a complete classification of the smooth three-folds in the Grassmann variety of lines in P-4, for which the restriction of the universal quotient bundle is a direct sum of two line bundles. For this purpose we use the geometrical interpretation of the splitting of the quotient bundle as well as the meaning of the number of the independent global sections of each of its summands.