Explanipedia

On some freeness-type properties for line arrangements Open

Takuro Abe, Denis Ibadula, Anca Măcinic · 2021

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.

Freeness for 13 lines arrangements is combinatorial Open

Alexandru Dimca, Denis Ibadula, Anca Măcinic · 2019

Freeness and near freeness are combinatorial for line arrangements in\n small degrees Open

Alexandru Dimca, Denis Ibadula, Anca Măcinic · 2017

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…

Freeness and near freeness are combinatorial for line arrangements in small degrees Open

Alexandru Dimca, Denis Ibadula, Anca Măcinic · 2017

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…

Numerical invariants and moduli spaces for line arrangements Open

Alexandru Dimca, Denis Ibadula, Anca Măcinic · 2017

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…

THE HOLOMORPHY CONJECTURE FOR NONDEGENERATE SURFACE SINGULARITIES Open

Wouter Castryck, Denis Ibadula, Ann Lemahieu · 2016

The holomorphy conjecture roughly states that Igusa’s zeta function associated to a hypersurface and a character is holomorphic on $\mathbb{C}$ whenever the order of the character does not divide the order of any eigenvalue of the local mo…

Pencil type line arrangements of low degree: classification and monodromy Open

Alexandru Dimca, Denis Ibadula, Anca Măcinic · 2016

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-…

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