A generalization of the $\Delta$-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 Δ -genus. In this paper we introduce the i -th Δ -genus Δ i ( X , L ) for every integer i with 0 ≤ i ≤ n = dim X . This is a generalization of the Δ -genus. Furthermore we study some properties of Δ i ( X , L ) and we will propose some problems.