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.
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Explicit formulas express dimension and degree of singular subschemes of hypersurfaces in P^n via Betti numbers of the Jacobian algebra's minimal resolution, yielding new restrictions on those numbers and a definition for homologically strictly plus-one generated hypersurfaces with singular locus di
A closed formula expresses the Hilbert polynomial of the Jacobian algebra of a reduced surface in P^3 in terms of its graded Betti numbers, giving new necessary conditions when singularities are isolated.
Provides numerical restrictions for plus-one generated conic arrangements with defect 3 and catalogs Ziegler pairs up to degree 6.
Investigates Fitting ideals of Tjurina ideals for non-quasi-homogeneous plane curve singularities, highlighting special properties when Milnor-Tjurina difference is at most 2.
citing papers explorer
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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.
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On the degree of the singular subscheme of hypersurfaces in ${\mathbb P}^n$
Explicit formulas express dimension and degree of singular subschemes of hypersurfaces in P^n via Betti numbers of the Jacobian algebra's minimal resolution, yielding new restrictions on those numbers and a definition for homologically strictly plus-one generated hypersurfaces with singular locus di
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Graded Betti numbers of the Jacobian algebra of surfaces in $\mathbb P^3$
A closed formula expresses the Hilbert polynomial of the Jacobian algebra of a reduced surface in P^3 in terms of its graded Betti numbers, giving new necessary conditions when singularities are isolated.
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On homological properties of conic-line arrangements with simple singularities
Provides numerical restrictions for plus-one generated conic arrangements with defect 3 and catalogs Ziegler pairs up to degree 6.
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Plane curve singularities and Fitting ideals
Investigates Fitting ideals of Tjurina ideals for non-quasi-homogeneous plane curve singularities, highlighting special properties when Milnor-Tjurina difference is at most 2.