Joint Mathematics Colloquium
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Abstract |
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| We consider hyperplane arrangements that have
logarithmic vector fields (or logarithmic derivations) of degree one or
two, and which are not multiple of the Euler derivation. For the degree
one case, by the means of edge ideals, we can show that the condition
to have such a linear logarithmic derivation is equivalent to the
hyperplane arrangement being reducible (i.e., Cartesian product of
smaller arrangements). For the degree two case, as expected, the
situation is not very nice. Though we were able to classify all
hyperplane arrangements in the projective plane (line arrangements)
that have a quadratic logarithmic derivation, the proof nor the
classification do not give any insights on what happens in general.
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