On the sectional invariants of polarized manifolds

Let (X,L)(X,L) be a polarized manifold of dimension nn. In this paper, for any integer ii with 0≤i≤n0≤i≤n we introduce the notion of the iith sectional invariant of (X,L)(X,L). We define the iith sectional Euler number ei(X,L)ei(X,L), the iith sectional Betti number bi(X,L)bi(X,L), and the iith sectional Hodge number hij,i−j(X,L) of type (j,i−j)(j,i−j) of (X,L)(X,L) and we will study some properties of these.