For d<9 line arrangements the intersection lattice determines the exponent data; six Ziegler pairs with d=10 share the same lattice, Jacobian degree and Milnor algebra Hilbert function but have different minimal graded free resolutions.
Dimca, On the module of derivations of a line arrangement,arXiv:2503.01624, to appear inPubl
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On Ziegler pairs of line arrangements: from non-existence to abundance
For d<9 line arrangements the intersection lattice determines the exponent data; six Ziegler pairs with d=10 share the same lattice, Jacobian degree and Milnor algebra Hilbert function but have different minimal graded free resolutions.