7 papers · 1 filter
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…
A note on combinatorial type and splitting invariants of plane curves
Taketo Shirane
Splitting invariants describe how a plane curve "splits" by the pull-back under a Galois cover over the projective plane whose branch locus contains no component of the plane curve…
Poncelet's closure theorem and the embedded topology of conic-line arrangements
Shinzo Bannai, Ryosuke Masuya, Taketo Shirane +2
In this paper, we consider conic-line arrangements that arise from Poncelet's closure theorem. We study unramified double covers of the union of two conics, that are induced by a $…
The realization space of a certain conic line arrangement of degree 7 and a -equivalent Zariski pair
Meirav Amram, Shinzo Bannai, Taketo Shirane +2
In this paper, we continue the study of the embedded topology of plane algebraic curves. We study the realization space of conic line arrangements of degree with certain fixed…
Torsion divisors of plane curves with maximal flexes and Zariski pairs
E. Artal Bartolo, S. Bannai, T. Shirane +1
There is a close relationship between the embedded topology of complex plane curves and the (group-theoretic) arithmetic of elliptic curves. In a recent paper, we studied the topol…
Galois covers of graphs and embedded topology of plane curves
Taketo Shirane
The splitting number is effective to distinguish the embedded topology of plane curves, and it is not determined by the fundamental group of the complement of the plane curve. In t…