论文标题
仿射空间的模棱两可
Equivariant completions of affine spaces
论文作者
论文摘要
我们调查了仿射空间$ \ mathbb {c}^n $的开放嵌入中的最新结果，以使vector grout $ \ mathbb {g} _a^n $ on $ \ mathbb {c}^n $ translations transpos of $ mathbbbbbbbbbbbbbb n o $ \ mathbbbbbbbb = g}我们从Hassett-tschinkel对应关系开始，描述了$ \ Mathbb {C}^n $的ecurivariant嵌入到投影空间中，并将其嵌入到投射性超胸膜中的概括。进一步的部分涉及嵌入到国旗品种中及其变性，完整的复曲面品种以及某些类型的Fano品种。
We survey recent results on open embeddings of the affine space $\mathbb{C}^n$ into a complete algebraic variety $X$ such that the action of the vector group $\mathbb{G}_a^n$ on $\mathbb{C}^n$ by translations extends to an action of $\mathbb{G}_a^n$ on $X$. We begin with Hassett-Tschinkel correspondence describing equivariant embeddings of $\mathbb{C}^n$ into projective spaces and give its generalization for embeddings into projective hypersurfaces. Further sections deal with embeddings into flag varieties and their degenerations, complete toric varieties, and Fano varieties of certain types.
