论文标题
Noether-Lefschetz组件的复合界限
Codimension bounds for the Noether-Lefschetz components for toric varieties
论文作者
论文摘要
对于射影的简单平滑型超曲面$ x $，在一个投影型简单的旋转复合品种$ p $中，形态$ i：h^p（p）\ to H^p（x）$ to the Cannepusive to $ p = d $，对于$ p = d $，对于$ p <d-1 $，$ d = dim d = dim d = dim p = dim \ p $。这允许人们将Noether-Lefschetz基因座$NL_β$定义为$β$的准平滑性超曲面的基因座，使得$ i $ $ i $作用于中代代数共同体，不是同形的。 In this paper we prove that, under some assumptions, if $dim P =2k+1$ and $kβ-β_0=nη$ $(n\in\mathbb N)$, where $η$ is the class of a 0-regular ample divisor, and $β_0$ is the anticanonical class, then every irreducible component $V$ of the Noether-Lefschetz locus quasi-smooth $β$的高度曲面会满足$ n+1 \ leq codim \ v \ leq h^{k-1，k+1}（x）$。
For a quasi-smooth hyper-surface $X$ in a projective simplicial toric variety $P$, the morphism $i:H^p(P) \to H^p(X)$ induced by the inclusion is injective for $p=d$ and an isomorphism for $p<d-1$, where $d=dim\ P$. This allows one to define the Noether-Lefschetz locus $NL_β$ as the locus of quasi-smooth hypersurfaces of degree $β$ such that $i$ acting on the middle algebraic cohomology is not an isomorphism. In this paper we prove that, under some assumptions, if $dim P =2k+1$ and $kβ-β_0=nη$ $(n\in\mathbb N)$, where $η$ is the class of a 0-regular ample divisor, and $β_0$ is the anticanonical class, then every irreducible component $V$ of the Noether-Lefschetz locus quasi-smooth hypersurfaces of degree $β$ satifies the bounds $n+1\leq codim\ V \leq h^{k-1,k+1}(X)$.
