JournalsrsmupVol. 125pp. 107–117

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

  • Yoshiaki Fukuma

    Kochi University, Japan
On Quasi-Polarized Manifolds Whose Sectional Genus is Equal to the Irregularity cover
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Abstract

Let (X,L)(X,L) be a quasi-polarized manifold of dimension nn. In our previous paper, we proved that if dimX=3\dim X=3 and h0(L)2h^{0}(L)\geq 2, then g(X,L)h1(OX)g(X,L)\geq h^{1}(\mathcal{O}_{X}) holds. Here g(X,L)g(X,L) denotes the sectional genus of (X,L)(X,L). In this paper, we give the classification of quasi-polarized 33-folds (X,L)(X,L) with h0(L)3h^{0}(L)\geq 3 and g(X,L)=h1(OX)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)(X,L) with dim\mboxBsL=1\dim \mbox{Bs}|L|=1, h0(L)nh^{0}(L)\geq n and g(X,L)=h1(OX)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