Anca Măcinic
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View article: On plus-one generated conic-line arrangements with simple singularities
On plus-one generated conic-line arrangements with simple singularities Open
In this paper, we study plus-one generated arrangements of conics and lines in the complex projective plane with simple singularities. We provide several degree-wise classification results that allow us to construct explicit examples of su…
View article: Deletion-addition of a smooth conic for free curves
Deletion-addition of a smooth conic for free curves Open
We describe the behaviour of a free reduced plane projective curve with respect to the deletion, respectively addition, of a smooth conic. These results apply in particular to conic-line arrangements. We present some obstructions to the ge…
View article: Addition-deletion results for plus-one generated curves
Addition-deletion results for plus-one generated curves Open
In the recent paper A. Dimca proves that when one adds to or deletes a line from a free curve the resulting curve is either free or plus-one generated. We prove the converse statements, we give an additional insight into the original delet…
View article: On plus-one generated conic-line arrangements with simple singularities
On plus-one generated conic-line arrangements with simple singularities Open
In this paper we study plus-one generated arrangements of conics and lines in the complex projective plane with simple singularities. We provide several degree-wise classification results that allow us to construct explicit examples of suc…
View article: A geometric perspective on plus-one generated arrangements of lines
A geometric perspective on plus-one generated arrangements of lines Open
We give a geometric characterisation of plus-one generated projective line arrangements that are next-to-free. We present new succinct proofs, via associated line bundles, for some properties of plus-one generated projective line arrangeme…
View article: On torsion freeness for the decomposable Orlik-Solomon algebra
On torsion freeness for the decomposable Orlik-Solomon algebra Open
We prove the torsion freeness of the decomposable Orlik--Solomon algebra of a simple matroid on ground set $[n]$. In the class of hypersolvable \& non-supersolvable complex hyperplane arrangements, the torsion freeness, in a certain degree…
View article: On some freeness-type properties for line arrangements
On some freeness-type properties for line arrangements Open
By way of Ziegler restrictions we study the relation between nearly free plane arrangements and combinatorics and we give a Yoshinaga-type criterion for plus-one generated plane arrangements.
View article: Freeness for 13 lines arrangements is combinatorial
Freeness for 13 lines arrangements is combinatorial Open
View article: Freeness and near freeness are combinatorial for line arrangements in\n small degrees
Freeness and near freeness are combinatorial for line arrangements in\n small degrees Open
We prove Terao conjecture saying that the freeness is determined by the\ncombinatorics for arrangements of 13 lines in the complex projective plane and\nthat the property of being nearly free is combinatorial for line arrangements\nof up t…
View article: Freeness and near freeness are combinatorial for line arrangements in small degrees
Freeness and near freeness are combinatorial for line arrangements in small degrees Open
We prove Terao conjecture saying that the freeness is determined by the combinatorics for arrangements of 13 lines in the complex projective plane and that the property of being nearly free is combinatorial for line arrangements of up to 1…
View article: Modular Equalities for Complex Reflection Arrangements
Modular Equalities for Complex Reflection Arrangements Open
We compute the combinatorial Aomoto-Betti numbers \beta_{p}(\mathcal A) of a complex reflection arrangement. When \mathcal A has rank at least 3, we find that \beta_{p}(\mathcal A)\leq 2 , for all primes p . Moreover, \beta_{p}(\mathcal A)…
View article: Numerical invariants and moduli spaces for line arrangements
Numerical invariants and moduli spaces for line arrangements Open
Using several numerical invariants, we study a partition of the space of line arrangements in the complex projective plane, given by the intersection lattice types. We oer also a new characterization of the free plane curves using the Cast…
View article: Pencil type line arrangements of low degree: classification and monodromy
Pencil type line arrangements of low degree: classification and monodromy Open
The complete classification of (3,3)-nets and of (3,4)-nets with only double and triple points is given. Up to lattice isomorphism, there are exactly 3 effective possibilities in each case, and some of these provide new examples of pencil-…
View article: On the Second Nilpotent Quotient of Higher Homotopy Groups, for Hypersolvable Arrangements
On the Second Nilpotent Quotient of Higher Homotopy Groups, for Hypersolvable Arrangements Open
We examine the first nonvanishing higher homotopy group, $\\pi _p$, of the complement of a hypersolvable, nonsupersolvable, complex hyperplane arrangement, as a module over the group ring of the fundamental group, $\\mathbb {Z}\\pi _1$. We…