论文标题
对对数形式的删除限制在多部位上
Deletion-Restriction for Logarithmic Forms on Multiarrangements
论文作者
论文摘要
我们考虑对数差分形式在删除和限制的运作下的编排和多动式的行为，从而延长了GünterZiegler的早期工作。对数形式对超平面形式的限制可能是或不会汇总的，我们根据对数形式和派生的交换代数来衡量汇总的失败。我们发现对数矢量场的限制双重概念的行为相似但不等。一个主要结果是，如果安排是免费的，则通过添加超平面获得的任何安排具有“双重强度加一个生成”的属性。一个应用程序是第一作者的主要结果证明了在免费安排中添加超平面时表征的纸张结果。进一步的应用是解决由于Ziegler的两个猜想，我们将其延迟到续集。
We consider the behaviour of logarithmic differential forms on arrangements and multiarrangements of hyperplanes under the operations of deletion and restriction, extending early work of Günter Ziegler. The restriction of logarithmic forms to a hyperplane may or may not be surjective, and we measure the failure of surjectivity in terms of commutative algebra of logarithmic forms and derivations. We find that the dual notion of restriction of logarithmic vector fields behaves similarly but inequivalently. A main result is that, if an arrangement is free, then any arrangement obtained by adding a hyperplane has the "dual strongly plus-one generated" property. One application is another proof of a main result of a paper by the first author characterizing when adding a hyperplane to a free arrangement remains free. A further application is to resolve two conjectures due to Ziegler, which we defer to a sequel.
