## Kodai Mathematical Journal

### Sectional geometric genera for ample vector bundles

Hironobu Ishihara

#### Abstract

Two invariants, called the $c_1$-sectional geometric genus and the $\co(1)$-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 $c_1$-sectional genus and the $\co(1)$-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 $c_1$ or $\co(1)$-sectional geometric genus under the spannedness condition for ample vector bundles.

#### Article information

Source
Kodai Math. J., Volume 27, Number 1 (2004), 74-87.

Dates
First available in Project Euclid: 21 May 2004

https://projecteuclid.org/euclid.kmj/1085143790

Digital Object Identifier
doi:10.2996/kmj/1085143790

Mathematical Reviews number (MathSciNet)
MR2042792

Zentralblatt MATH identifier
1066.14019

#### Citation

Ishihara, Hironobu. Sectional geometric genera for ample vector bundles. Kodai Math. J. 27 (2004), no. 1, 74--87. doi:10.2996/kmj/1085143790. https://projecteuclid.org/euclid.kmj/1085143790