JournalsprimsVol. 48, No. 1pp. 83–106

A Numerical Characterization of Polarized Manifolds (X,L)(X,\mathcal{L}) with KX=(ni)LK_{X}=-(n-i)\mathcal{L} by the iith Sectional Geometric Genus and the iith Δ\Delta-genus

  • Yoshiaki Fukuma

    Kochi University, Japan
A Numerical Characterization of Polarized Manifolds $(X,\mathcal{L})$ with $K_{X}=-(n-i)\mathcal{L}$ by the $i$th Sectional Geometric Genus and the $i$th $\Delta$-genus cover
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Abstract

Let (X,L)(X,\mathcal{L}) be a polarized manifold of dimension nn. In this paper, by using the iith sectional geometric genus and the iith Δ\Delta-genus, we will give a numerical characterization of (X,L)(X,\mathcal{L}) with KX=(ni)LK_{X}=-(n-i)\mathcal{L} for the following cases (i) i=2i=2, (ii) i=3i=3 and n5n\geq 5, (iii) \mboxmax{2,dim\mboxBsL+2}in1\mbox{max}\{ 2, \dim \mbox{Bs}|\mathcal{L}|+2\}\leq i\leq n-1.

Cite this article

Yoshiaki Fukuma, A Numerical Characterization of Polarized Manifolds (X,L)(X,\mathcal{L}) with KX=(ni)LK_{X}=-(n-i)\mathcal{L} by the iith Sectional Geometric Genus and the iith Δ\Delta-genus. Publ. Res. Inst. Math. Sci. 48 (2012), no. 1, pp. 83–106

DOI 10.2977/PRIMS/62