On Zariski's pairs of m-th canonical discriminant curves
Abstract
Description
In this note we give examples of Zariski's pairs $B_{1,m}, B_{2,m}$ ($m \in N$ and $m \geq 5$) 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
4 pages, LaTeX2e