# On Quasi-Polarized Manifolds Whose Sectional Genus is Equal to the Irregularity

### Yoshiaki Fukuma

Kochi University, Japan

## Abstract

Let $(X,L)$ be a quasi-polarized manifold of dimension $n$.In our previous paper, we proved that if $\dim X=3$ and $h^{0}(L)\geq 2$, then$g(X,L)\geq h^{1}(\mathcal{O}_{X})$ holds. Here $g(X,L)$ denotes the sectional genus of $(X,L)$.In this paper, we give the classification of quasi-polarized $3$-folds $(X,L)$ with $h^{0}(L)\geq 3$ and $g(X,L)=h^{1}(\mathcal{O}_{X})$.Moreover as an application of this result, we also give the classification of polarized manifolds $(X,L)$ with $\dim \mbox{Bs}|L|=1$, $h^{0}(L)\geq n$ and $g(X,L)=h^{1}(\mathcal{O}_{X})$.

## Cite this article

Yoshiaki Fukuma, On Quasi-Polarized Manifolds Whose Sectional Genus is Equal to the Irregularity. Rend. Sem. Mat. Univ. Padova 125 (2011), pp. 107–117

DOI 10.4171/RSMUP/125-7