# Rendiconti del Seminario Matematico della Università di Padova

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**Volume 125, 2011, pp. 107–117**

**DOI: 10.4171/RSMUP/125-7**

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

Yoshiaki Fukuma^{[1]}(1) Kochi University, Japan

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 $g(X,L)=h^{1}(\mathcal{O}_{X})$.

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Fukuma Yoshiaki: On Quasi-Polarized Manifolds Whose Sectional Genus is Equal to the Irregularity. *Rend. Sem. Mat. Univ. Padova* 125 (2011), 107-117. doi: 10.4171/RSMUP/125-7