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arXiv 1003.5736math.AG
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拟极化流形的第二截几何亏格的注记及其应用

Remarks on the second sectional geometric genus of quasi-polarized manifolds and their applications

Yoshiaki Fukuma

备注：
20 pages. We improved some results and corrected some errata in the second version of this paper
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摘要：

在我们以前的文章中，我们研究了$n$维极化流形$(X,L)$的第二截面几何亏格$g_{2}(X,L)$的一个下界，并利用这个下界研究了用$t\geq 2$构造的$K_{X}+tL$的整体截面的维数.在本文中，我们考虑的情况下，$(X,L)$是一个拟极化流形。首先，我们将证明以下情况下的$g_{2}(X,L)\geq h^{1}(\mathcal{O}_{X})$：（a）$n=3$，$κ(X)=-\infty$和$κ(K_{X}+L)\geq 0$。(b)$n\geq 3$和$κ(X)\geq 0$。此外，利用这个不等式，我们将研究$h^{0}(K_{X}+tL)$的情况下，$(X,L)$是准极化的3倍。

英文摘要：

In our previous papers, we investigated a lower bound for the second sectional geometric genus $g_{2}(X,L)$ of $n$-dimensional polarized manifolds $(X,L)$ and by using these, we studied the dimension of global sections of $K_{X}+tL$ with $t\geq 2$. In this paper, we consider the case where $(X,L)$ is a quasi-polarized manifold. First we will prove $g_{2}(X,L)\geq h^{1}(\mathcal{O}_{X})$ for the following cases: (a) $n=3$, $κ(X)=-\infty$ and $κ(K_{X}+L)\geq 0$. (b) $n\geq 3$ and $κ(X)\geq 0$. Moreover, by using this inequality, we will study $h^{0}(K_{X}+tL)$ for the case where $(X,L)$ is a quasi-polarized 3-fold.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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