Invariants of ample line bundles on projective varieties and their applications, III

Abstract

Let X be a smooth complex projective variety of dimension n and let L₁, ..., L_n–i be ample line bundles on X, where i is an integer with 0 ≤ i ≤ n – 1. In the first part, we defined the ith sectional geometric genus g_i(X, L₁, ..., L_n–i) and the ith sectional H-arithmetic genus χ_i^H(X, L₁, ..., L_n–i) of (X, L₁, ..., L_n–i). In this third part, we will investigate g₂(X, L₁, ..., L_n–2) and χ₂^H(X, L₁, ..., L_n–2). Moreover we will give some applications of the sectional invariants of multi-polarized manifolds.