多超平面排列上对数形式的删除-限制
Deletion-Restriction for Logarithmic Forms on Multiarrangements
AI总结：
研究超平面排列与多排列中对数微分形式在删除和限制操作下的行为，通过交换代数度量满射性缺失，并证明自由排列添加超平面后具有“对偶强加一生成”性质。
摘要：
我们考虑超平面排列与多排列中对数微分形式在删除和限制操作下的行为，扩展了Günter Ziegler的早期工作。对数形式限制到一个超平面可能是满射也可能不是，我们通过对数形式和导子的交换代数来度量满射性的缺失。我们发现对数向量场限制的对偶概念行为相似但不等价。一个主要结果是，如果一个排列是自由的，那么通过添加一个超平面得到的任何排列都具有“对偶强加一生成”性质。一个应用是给出了第一作者一篇论文中关于何时向自由排列添加超平面仍保持自由的主要结果的另一个证明。另一个应用是解决了Ziegler提出的两个猜想，我们将这些内容推迟到后续文章。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
