For a normal crossing arrangement of the n+1 coordinate hyperplanes and a generic smooth hypersurface of degree e, the Jacobian algebra has a Koszul-type minimal resolution with exponents all equal to e+1.
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On the Jacobian syzygies for generic toric models
For a normal crossing arrangement of the n+1 coordinate hyperplanes and a generic smooth hypersurface of degree e, the Jacobian algebra has a Koszul-type minimal resolution with exponents all equal to e+1.