Momoko Yamamoto (Tokyo Metropolitan University)
Title: On the topology of arrangements for a smooth plane quartic and its bitangent lines
Abstract: Let $Q$ be a smooth plane quartic. It is known that $Q$ has $28$ bitangent lines
$L_{1}, \ldots , L_{28}$. For $I \subset \{ 1, \ldots , 28 \}$,
we put $L_{I}:=\sum_{i \in I}L_{i}$. In this talk,
we introduce a new method based on connected numbers
defined by T. Shirane and subarrangements of $Q+L_{I}$
in order to distinguish the embedded topology of $Q+L_{I}$ when $|I|=3, 4$.
As an application,
we construct Zariski pair of degree $7$ (resp. Zariski triple of degree $8$),
which consists of $Q$ and three (resp. four) bitangent lines to $Q$.
These results are joint work with Shinzo Bannai and Hiroo Tokunaga.