13 citations · 22 across the 11 of their papers we have counts for
4 papers · 1 filter
Nodal curves with a contact-conic and Zariski pairs
Shinzo Bannai, Taketo Shirane
In this present paper, we study the splitting of nodal plane curves with respect to contact conics. We define the notion of splitting type of such curves and show that it can be us…
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 note on splitting numbers for Galois covers and -equivalent Zariski -plets
Taketo Shirane
In this paper, we introduce \textit{splitting numbers} of subvarieties in a smooth variety for a Galois cover, and prove that the splitting numbers are invariant under certain home…