论文标题
阿贝利亚品种中一般超曲面的规范图
Canonical Maps of general Hypersurfaces in Abelian Varieties
论文作者
论文摘要
本文的主要理论是，对于一对（a，x）的一般$（a，x）$（ample）hypersurface $ x $ in Abelian品种中的$ a $，如果$ x $给出的偏光不primplation，则规范地图$φ_x$ $ x $是birational of tomational of thrimations of the Imagation of thrimations birational（即pfaffian $ d $ $ d $ $ $ $ 1 $）。 我们还表明，设置$ g = dim（a）$，而让$ d $是$ x $给出的两极分化的pfaffian，那么，如果$ x $且$ x $很光滑并且$$φ_x：x \ rightarrow \ mathbb {p}^{n：= g + d-2} $ G + D-2 \ GEQ 2 \ DIM（X） + 1. $ 我们还制定了以下有趣的猜想，这是由第二作者的工作激励的：如果$ d \ geq g + 1，$，那么，对于一般对$（a，x）$，$φ_x$是一个嵌入。
The main theorem of this paper is that, for a general pair $(A,X)$ of an (ample) Hypersurface $X$ in an Abelian Variety $A$, the canonical map $Φ_X$ of $X$ is birational onto its image if the polarization given by $X$ is not principal (i.e., its Pfaffian $d$ is not equal to $1$). We also show that, setting $g = dim (A)$, and letting $d$ be the Pfaffian of the polarization given by $X$, then if $X$ is smooth and $$Φ_X : X \rightarrow \mathbb{P}^{N:=g+d-2}$$ is an embedding, then necessarily we have the inequality $ d \geq g + 1$, equivalent to $N : = g+d-2 \geq 2 \ dim(X) + 1.$ We also formulate the following interesting conjecture, motivated by work of the second author: if $ d \geq g + 1,$ then, for a general pair $(A,X)$, $Φ_X$ is an embedding.
