A generalization of the \vD-genus of quasi-polarized varieties

Abstract

Let (X, L) be a quasi-polarized variety defined over the complex number field. Then there are several invariants of (X, L), for example, the sectional genus and the \vD-genus. In this paper we introduce the i-th \vD-genus \vD_i(X, L) for every integer i with 0≤ i≤ n=\dim X. This is a generalization of the \vD-genus. Furthermore we study some properties of \vD_i(X, L) and we will propose some problems.