论文标题
Lefschetz二元性二元性
Lefschetz duality for local cohomology
论文作者
论文摘要
自1974年Peskine和Szpiro的论文以来，通过完整的交集以及更普遍地通过Gorenstein品种的联络理论已成为交换代数和代数几何形状的标准工具套件，从而可以比较连接品种的代数特征。在本文中，我们通过Quasi-Gorenstein品种开发了一个联络理论，这比Gorenstein品种要广泛得多：认为Quasi-Gorenstein Rings是Gorenstein Rings对歧管而言，这并不是误导性的。作为应用，我们得出了准 - 戈伦斯坦子空间的连接性属性，使贝内德蒂（Benedetti）和第二作者概括了先前的结果，并通过斯坦利 - 赖斯纳（Stanley-Reisner）的对应关系推断出经典的拓扑Lefschetz偶性。
Since the 1974 paper by Peskine and Szpiro, liaison theory via complete intersections, and more generally via Gorenstein varieties, has become a standard tool kit in commutative algebra and algebraic geometry, allowing to compare algebraic features of linked varieties. In this paper we develop a liaison theory via quasi-Gorenstein varieties, a much broader class than Gorenstein varieties: it is not misleading to think that quasi-Gorenstein rings are to Gorenstein rings as manifolds are to spheres. As applications, we derive a connectedness property of quasi-Gorenstein subspace arrangements generalizing previous results by Benedetti and the second author, and we deduce the classical topological Lefschetz duality via the Stanley-Reisner correspondence.
