Topological properties of certain incomplete regular intersections

The author announces some, mostly topological, results on certain nonsingular complex projective varieties. These varieties may be represented as regular intersections of hypersurfaces which number equals the codimension of the variety plus $1$. Formulas are given for its Euler characteristic and, in the case of codimension $2$, for the Todd genus and the signature. These formulas contain the degree of the variety and degrees of its equations. So called determinantali loci yield a stock of such varieties. As to dimensions $2$ and $3$ the iff-comdition for such varieties to be a determinantal locus is described by a simple inequality involving the degree of the variety and degrees of its equations. On the other hand, all such varieties of dimension not less than its codimension and greater than $3$ turn out to be regular complete intersections.