Abstract

Let X be a compact complex manifold of dimension n ≥ 2 and E an ample vector bundle of rank r < n on X. As the continuation of Part I, we further study the properties of g(X,E) that is an invariant for pairs (X,E) and is equal to curve genus when r = n − 1. Main results are the classifications of (X,E) with g(X,E) = 2 (resp. 3) when E has a regular section (resp. E is ample and spanned) and 1 < r < n − 1.

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