Topological properties of certain incomplete regular intersections (Q799752)

Varieties are studied which are regular intersections of hypersurfaces of number codimension plus 1. The author gives formulas for the Euler characteristic and, in the case of codimension 2, for the Todd genus and the signature. The determinantal varieties are such incomplete intersections. As a list of examples curves in the complex projective 3- space, surfaces in 4-space and 3-varieties in 5-space are considered and conditions are given for it to be determinantal loci or not.