论文标题
在非传播的交叉点和本地交叉点上
On non-proper intersections and local intersection numbers
论文作者
论文摘要
给定纯维（广义）循环$μ_1$和$μ_2$在复杂的歧管$ y $上，我们引入了产品$μ_1\ diamond_ {y}μ_2$，这是一个广义周期，其多数循环在每个点上都是本地点的数字。 ％ 如果$ y $是投射的，则给出一个非常宽敞的线条束$ l \ y $，我们定义了产品$μ_1\blμ_2$，其每个点的多重性也与本地交叉点数一致。此外，只要$μ_1$和$μ_2$有效，则该产品满足了Bézout的不平等。如果$ i \ colon y \ to \ pk^n $是一种嵌入，以至于$ i^*\ ok（1）= l $，则可以将$μ__1\ blμ_2$表示为Stückrad-vogel Cycles $ \ pk^n $的平均值。 $ \ di_y $和$ \ bl $之间有很明确的关系。
Given pure-dimensional (generalized) cycles $μ_1$ and $μ_2$ on a complex manifold $Y$ we introduce a product $μ_1\diamond_{Y} μ_2$ that is a generalized cycle whose multiplicities at each point are the local intersection numbers at the point. % If $Y$ is projective, then given a very ample line bundle $L\to Y$ we define a product $μ_1\bl μ_2$ whose multiplicities at each point also coincide with the local intersection numbers. In addition, provided that $μ_1$ and $μ_2$ are effective, this product satisfies a Bézout inequality. If $i\colon Y\to \Pk^N$ is an embedding such that $i^*\Ok(1)=L$, then $μ_1\bl μ_2$ can be expressed as a mean value of Stückrad-Vogel cycles on $\Pk^N$. There are quite explicit relations between $\di_Y$ and $\bl$.
