Taketo Shirane

An invariant of plane curves through Galois covers and Zariski pairs

The number of irreducible components of the pull-back of an irreducible
plane curve by a Galois cover over the projective plane is called the
splitting number of the irreducible plane curve for the Galois cover. The
splitting number is effective to distinguish the embedded topology of plane
curves. In this talk, we consider a number for plane curves (possibly
reducible) which is similar to the splitting number. As its application, we
construct Zariski $k$-plets given by arrangements of three lines and a
smooth curve, which are extension of Artal arrangements.