Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4646796 | Discrete Mathematics | 2016 | 8 Pages |
Abstract
In these notes we study hyperplane arrangements having at least one logarithmic derivation of degree two that is not a combination of degree one logarithmic derivations. It is well-known that if a hyperplane arrangement has a linear logarithmic derivation not a constant multiple of the Euler derivation, then the arrangement decomposes as the direct product of smaller arrangements. The next natural step would be to study arrangements with non-trivial quadratic logarithmic derivations. On this regard, we present a computational lemma that leads to a full classification of hyperplane arrangements of rank 3 having such a quadratic logarithmic derivation. These results come as a consequence of looking at the variety of the points dual to the hyperplanes in such special arrangements.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Åtefan O. TohaËneanu,