Abstract
Let X be a smooth projective variety of dim X=n over the complex number field and let ε be an ample vector bundle of rank r on X with 1<r<n. In this paper, we introduce the notion of the i-th cr-sectional geometric genus of (X, E) for every integer i with O<i<n-r. This is a generalization of the cr-sectional genus which was defined by Ishihara. Furthermore we study some of its properties.
