论文标题
部分可观测时空混沌系统的无模型预测
The Kähler different of a 0-dimensional scheme
论文作者
论文摘要
给定投影$ n $ -space $ \ mathbb {p}^n_k $在field $ k $上的投影$ n $ -space $ \ space $ \ mathbb {x} $的0维方案，我们有兴趣研究$ \ mathbb {x} $的kähler。使用Kähler不同，我们表征了$ \ Mathbb {X} $的通用位置和Cayley-Bacharach属性。当$ \ mathbb {x} $处于通用位置时，我们证明了有关算术的Gorenstein方案的Apéry-Gorenstein-Samuel定理的广义版。我们还根据Kähler不同和Cayley-Bacharach属性来表征0维完成的交集。
Given a 0-dimensional scheme $\mathbb{X}$ in the projective $n$-space $\mathbb{P}^n_K$ over a field $K$, we are interested in studying the Kähler different of $\mathbb{X}$ and its applications. Using the Kähler different, we characterize the generic position and Cayley-Bacharach properties of $\mathbb{X}$ in several certain cases. When $\mathbb{X}$ is in generic position, we prove a generalized version of the Apéry-Gorenstein-Samuel theorem about arithmetically Gorenstein schemes. We also characterize 0-dimensional complete intersections in terms of the Kähler different and the Cayley-Bacharach property.
