On Zariski's pairs of m-th canonical discriminant curves

Abstract

In this note we give examples of Zariski's pairs $B_{1,m},B_{2,m}$ ($m\in N$ and $m\ge 5$) of plane cuspidal curves such that (i) $B_{i,m}$ is the discriminant curve of a generic morphism $f_{i,m}:S_i\to P^2$, $i=1,2$, (ii) $S_1$ and $S_2$ are homeomorphic surfaces of general type, (iii) $f_{i,m}$ is given by linear three-dimensional subsystem of the mth canonical class of $S_i$.

4 pages, LaTeX2e