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Let X be a smooth complex projective variety of dimension n and let L1, . . . , Ln−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 gi(X, L1, . . . , Ln−i) and the ith sectional Harithmetic genus χi (X, L1, . . . , Ln−i) of (X, L1, . . . , Ln−i). In this third part, we will investigate g2(X, L1, . . . , Ln−2) and χ H 2 (X, L1, . . . , Ln−2). Moreover we will give some applications of the sectional invariants of multi-polarized manifolds.

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