The logarithmic forms of \(k\)-generic arrangements (Q1356262)
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scientific article; zbMATH DE number 1017585
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The logarithmic forms of \(k\)-generic arrangements |
scientific article; zbMATH DE number 1017585 |
Statements
The logarithmic forms of \(k\)-generic arrangements (English)
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8 January 1998
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The module \(\Omega^k({\mathcal A})\) of \(k\)-forms with at most logarithmic poles at an arrangement of hyperplanes \({\mathcal A}\) is generated by products of 1-forms \(d(\log \alpha_H)\) for hyperplanes \(H\in{\mathcal A}\) if and only if \({\mathcal A}\) is \((k+2)\)-generic, that is, if any family of \(k+2\) hyperplanes in \({\mathcal H}\) is transversal (every circuit has size at least \(k+3\)). This extends and completes results of the reviewer [Adv. Math. 76, 116-154 (1989; Zbl 0725.05032)].
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hyperplane arrangements
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modules of logarithmic forms
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\(k\)-forms
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generators
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