21 citations · 93 across the 36 of their papers we have counts for
51 papers
Plane curve singularities and Fitting ideals
Alexandru Dimca, Gabriel Sticlaru
In this note we investigate the Fitting ideals associated to the Tjurina ideal of a non quasi-homogeneous plane curve singularity. Special properties occur when the difference betw…
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…
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 correspo…
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…
A minimal resolution for the Jacobian ideal of a generic curve arrangement
Alexandru Dimca, Gabriel Sticlaru
We consider a nodal curve in the complex projective plane whose irreducible components are smooth. A minimal set of generators for the first and second syzygy modules…
On the Jacobian syzygies for generic toric models
Alexandru Dimca, Gabriel Sticlaru
To a generic hypersurface in the affine torus we associate a hypersurface arrangement in the projective space consisting of the coordinate h…
Bourbaki modules and the module of Jacobian derivations of projective hypersurfaces
Alexandru Dimca, Gabriel Sticlaru
Two properties of projective hypersurfaces related to the module of Jacobian derivations, namely being tame and being plus-one generated, are discussed in this paper. Tame hypersur…
Plus-one generated curves, Briançon-type polynomials and eigenscheme ideals
Alexandru Dimca, Gabriel Sticlaru
We define the minimal plus-one generated curves and prove a result explaining why they are the closest relatives of the free curves, after the nearly free curves. Then we look at t…
Curves with Jacobian syzygies of the same degree
Alexandru Dimca, Gabriel Sticlaru
In this notes we study complex projective plane curves whose graded module of Jacobian syzygies is generated by its minimal degree component. Examples of such curves include the sm…
From Pascal's Theorem to the geometry of Ziegler's line arrangements
Alexandru Dimca, Gabriel Sticlaru
Günter Ziegler has shown in 1989 that some homological invariants associated with the free resolutions of Jacobian ideals of line arrangements are not determined by combinatorics.…
On the Alexander polynomials of conic-line arrangements
Alexandru Dimca, Piotr Pokora, Gabriel Sticlaru
In the present paper we compute Alexander polynomials for certain classes of conic-line arrangements in the complex projective plane which are related to pencils. We prove two gene…
Construction of free curves by adding lines to a given curve
Alexandru Dimca, Giovanna Ilardi, Piotr Pokora +1
In the present note we construct new families of free plane curves starting from a curve and adding high order inflectional tangent lines of , lines joining the singularitie…
Addition-deletion results for the minimal degree of a Jacobian syzygy of a union of two curves
A. Dimca, G. Ilardi, G. Sticlaru
Let be a reduced curve in the complex projective plane. The minimal degree of a Jacobian syzygy for , which is the same as the minimal degree of a derivation ki…
On the birationality of the Hessian maps of quartic curves and cubic surfaces
Alexandru Dimca, Gabriel Sticlaru
We show that the hessian map of quartic plane curves is a birational morphism onto its image, thus bringing new evidence for a very interesting conjecture of Ciro Ciliberto and Gio…
Ramblings on the freeness of affine hypersurfaces
Alexandru Dimca, Gabriel Sticlaru
In this note we look at the freeness for complex affine hypersurfaces. If is such a hypersurface, and denotes the associated projective hypersurface, o…
Waring ranks of sextic binary forms via geometric invariant theory
Alexandru Dimca, Gabriel Sticlaru
We determine the Waring ranks of all sextic binary forms with complex coefficients using a Geometric Invariant Theory approach. Using the five basic invariants for sextic binary fo…
On the Bounded Negativity Conjecture and singular plane curves
Alexandru Dimca, Brian Harbourne, Gabriel Sticlaru
There are no known failures of Bounded Negativity in characteristic 0. In the light of recent work showing the Bounded Negativity Conjecture fails in positive characteristics for r…
Waring rank of binary forms, harmonic cross-ratio and golden ratio
Alexandru Dimca, Gabriel Sticlaru
We discuss the Waring rank of binary forms of degree 4 and 5, without multiple factors, and point out unexpected relations to the harmonic cross-ratio, j-invariants and the golden…
The Hessian polynomial and the Jacobian ideal of a reduced hypersurface in
Laurent Busé, Alexandru Dimca, Hal Schenck +1
For a reduced hypersurface of degree , the Castelnuovo-Mumford regularity of the Milnor algebra is well understood when is smooth, as…
Addition-deletion results for the minimal degree of logarithmic derivations of arrangements
Takuro Abe, Alexandru Dimca, Gabriel Sticlaru
We study the change of the minimal degree of a logarithmic derivation of a hyperplane arrangement under the addition or the deletion of a hyperplane, and give a number of applicati…
The 0-th Fitting ideal of the Jacobian module of a plane curve
Alexandru Dimca, Gabriel Sticlaru
We describe the 0-th Fitting ideal of the Jacobian module of a plane curve in terms of determinants involving the Jacobian syzygies of this curve. This leads to new characterizatio…
Waring rank of symmetric tensors, and singularities of some projective hypersurfaces
Alexandru Dimca, Gabriel Sticlaru
We show that if a homogeneous polynomial in variables has Waring rank , then the corresponding projective hypersurface has at most isolated singularities, and th…
Jacobian syzygies and plane curves with maximal global Tjurina numbers
Alexandru Dimca, Gabriel Sticlaru
First we give a sharp upper bound for the cardinal of a minimal set of generators for the module of Jacobian syzygies of a complex projective reduced plane curve . Next we d…