Abstract
Let X be a projective variety of dimension n defined over the field of complex numbers and let L1, ..., Ln-i be ample line bundles on X, where i is an integer with 0 ≤ i ≤ n. In this paper, first, we define some invariants called the ith sectional H-arithmetic genus, the ith sectional geometric genus and the ith sectional arithmetic genus of (X,L1, ..., Ln-i). These are considered to be a generalization of invariants which have been defined in our previous papers. Moreover we investigate some basic properties of these, which are used in the second part and the third part of this work.
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