English

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

Algebraic Geometry 2007-05-23 v1

Abstract

In this note we give examples of Zariski's pairs B1,m,B2,mB_{1,m}, B_{2,m} (mNm \in N and m5m \geq 5) of plane cuspidal curves such that (i) Bi,mB_{i,m} is the discriminant curve of a generic morphism fi,m:SiP2f_{i,m}:S_i \to P^2, i=1,2i=1, 2, (ii) S1S_1 and S2S_2 are homeomorphic surfaces of general type, (iii) fi,mf_{i,m} is given by linear three-dimensional subsystem of the mth canonical class of SiS_i.

Keywords

Cite

@article{arxiv.math/9807154,
  title  = {On Zariski's pairs of m-th canonical discriminant curves},
  author = {Vik. S. Kulikov},
  journal= {arXiv preprint arXiv:math/9807154},
  year   = {2007}
}

Comments

4 pages, LaTeX2e