抄録
Two invariants, called the c1-sectional geometric genus and the \mathcal{O}(1)-sectional geometric genus, are introduced for generalized polarized manifolds, i.e., pairs of a projective manifold and an ample vector bundle on it. They are generalizations of the c1-sectional genus and the \mathcal{O}(1)-sectional genus introduced by T. Fujita for generalized polarized manifolds. They are also generalizations of the sectional geometric genus introduced by Y. Fukuma for polarized manifolds. We classify generalized polarized manifolds of the smallest c1 or \mathcal{O}(1)-sectional geometric genus under the spannedness condition for ample vector bundles.
