论文标题
平滑品种的嵌入到线性代数群中
Existence of Embeddings of Smooth Varieties into Linear Algebraic Groups
论文作者
论文摘要
我们证明，每个尺寸$ d $的平滑仿射品种嵌入到每个简单的代数尺寸中，至少$ 2D+2 $。我们通过确定平稳仿射品种的嵌入到某些主要束的总空间中来做到这一点。对于后者，我们采用并基于卡利曼（Kaliman）引起的柔性仿射品种的参数横向结果。通过根据Bloch，Murthy和Szpiro调整基于Chow-group的论点，我们表明我们的结果是最佳的，可以提高绑定到$ 2D+1 $。为了研究我们嵌入方法的限制，我们使用合理同源性空间的合理同源组计算，并建立了复杂平滑品种合理同源性的统治结果。
We prove that every smooth affine variety of dimension $d$ embeds into every simple algebraic group of dimension at least $2d+2$. We do this by establishing the existence of embeddings of smooth affine varieties into the total space of certain principal bundles. For the latter we employ and build upon parametric transversality results for flexible affine varieties due to Kaliman. By adapting a Chow-group-based argument due to Bloch, Murthy, and Szpiro, we show that our result is optimal up to a possible improvement of the bound to $2d+1$. In order to study the limits of our embedding method, we use rational homology group calculations of homogeneous spaces and we establish a domination result for rational homology of complex smooth varieties.
