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

1998/07/27 by Vik. S. Kulikov, Kulikov, Vik. S.
Mathematics · #14J99 (Primary) 14H10 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14H10 #msc:14J99

paper · pdf · doi:10.48550/arxiv.math/9807154

4 pages, LaTeX2e

arxiv created 1998/07/27 · arxiv updated 2009/11/30

Abstract

In this note we give examples of Zariski's pairs B_1,m, B_2,m (m ∈ N and m ≥ 5) of plane cuspidal curves such that (i) B_i,m is the discriminant curve of a generic morphism f_i,m:S_i → P², i=1, 2, (ii) S₁ and S₂ 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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