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

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

1998-07-27

arxiv.org/abs/math/9807154v1

Mathematics

Algebraic Geometry

4 pages, LaTeX2e

Scientific paper

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 $S_i$.

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