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