21 citations · 45 across the 8 of their papers we have counts for
14 papers
Zariski pairs of conic-line arrangements with a unique conic
Shinzo Bannai, Benoît Guerville-Ballé, Taketo Shirane
In this note, we present two pairs of conic-line arrangements admitting a unique conic and that form Zariski pairs, both of degree . Their topologies are distinguished using the…
On the non-connectivity of moduli spaces of arrangements: the splitting-polygon structure
Benoît Guerville-Ballé
Questions that seek to determine whether a hyperplane arrangement property, be it geometric, arithmetic or topological, is of a combinatorial nature (that is determined by the inte…
The loop linking number of line arrangements
Benoît Guerville-Ballé
In his Ph.D. thesis, Cadegan-Schlieper constructs an invariant of the embedded topology of a line arrangement which generalizes the -invariant introduced by Artal, Flo…
Ineffectiveness of homotopical invariants on Nakanishi's 4-move conjecture
Benoît Guerville-Ballé, Juan Viu-Sos
A -move is a local operation for links consisting in replacing two parallel arcs by four half twists. At the present time, it is not known if this induces an unkotting operation…
Topology and homotopy of lattice isomorphic arrangements
Benoît Guerville-Ballé
We prove the existence of lattice isomorphic line arrangements having -equivalent or homotopy-equivalent complements and non homeomorphic embeddings in the complex projective…
Fundamental groups of real arrangements and torsion in the lower central series quotients
Enrique Artal Bartolo, Benoît Guerville-Ballé, Juan Viu-Sos
By using computer assistance, we prove that the fundamental group of the complement of a real complexified line arrangement is not determined by its intersection lattice, providing…
On the topology of arrangements of a cubic and its inflectional tangents
Shinzo Bannai, Benoît Guerville-Ballé, Taketo Shirane +1
A -Artal arrangement is a reducible algebraic curve composed of a smooth cubic and inflectional tangents. By studying the topological properties of their subarrangements, we…
Non-homotopicity of the linking set of algebraic plane curves
Benoît Guerville-Ballé, Taketo Shirane
The linking set is an invariant of algebraic plane curves introduced by Meilhan and the first author. It has been successfully used to detect several examples of Zariski pairs, i.e…
A linking invariant for algebraic curves
Benoît Guerville-Ballé, Jean-Baptiste Meilhan
We construct a topological invariant of algebraic plane curves, which is in some sense an adaptation of the linking number of knot theory. This invariant is shown to be a generaliz…
Multiplicativity of the -invariant and topology of glued arrangements
Benoît Guerville-Ballé
The invariant was first introduced by E. Artal, V. Florens and the author. Inspired by the idea of G. Rybnikov, we obtain a multiplicativity theorem…
Combinatorics of line arrangements and dynamics of polynomial vector fields
Benoît Guerville-Ballé, Juan Viu-Sos
Let be a real line arrangement and the module of --derivations. First, we give a dynamical interpretation of $\mathcal{D}(\mat…
Combinatorics of line arrangements and polynomial vector fields
Benoît Guerville-Ballé, Juan Viu-Sos
Let be a real line arrangement and the module of -derivations view as the set of polynomial vector fields which possess $\math…
An arithmetic Zariski 4-tuple of twelve lines
Benoît Guerville-Ballé
Using the invariant developed in [6], we differentiate four arrangements with the same combinatorial information but in different deformation classes. From these arrangements, we c…
A topological invariant of line arrangements
Enrique Artal Bartolo, Vincent Florens, Benoît Guerville-BallÉ
We define a new topological invariant of line arrangements in the complex projective plane. This invariant is a root of unity defined under some combinatorial restrictions for arra…