15 papers
On the Jacobian algebras of Ziegler pairs of plane arrangements
Alexandru Dimca, Piotr Pokora
We consider a Ziegler pair of plane arrangements, that is two plane arrangements and in the projective space , such that the int…
On the degree of the singular subscheme of hypersurfaces in
Alexandru Dimca, Gabriel Sticlaru
Explicit formulas determining the dimension and the degree of the singular subscheme of hypersurfaces in are given in terms of the graded Betti numbers of the minim…
Graded Betti numbers of the Jacobian algebra of surfaces in
Alexandru Dimca, Gabriel Sticlaru
We compute an explicit closed formula for the Hilbert polynomial of the Jacobian algebra of a reduced surface in in terms of the graded Betti numbers o…
Free line arrangements with low maximal multiplicity
Alexandru Dimca, Lukas Kühne, Piotr Pokora
Let $\A$ be a free arrangement of lines in the complex projective plane, with exponents . Let be the maximal multiplicity of points in $\A$. In this note, we d…
Graded Betti numbers of the Jacobian algebra and total Tjurina numbers of plane curves
Alexandru Dimca, Gabriel Sticlaru
In this paper we compute an explicit closed formula for the total Tjurina number of a reduced projective plane curve in terms of the graded Betti numbers of the corresp…
On type three complex plane curves
Alexandru Dimca, Gabriel Sticlaru
The type of a complex projective plane curve has been recently introduced by T. Abe, P. Pokora and the first author. In the same paper they have studied the type two curves. In thi…