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On the geometry of certain irreducible non-torus plane sextics

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  • Christophe Eyral, Denmark
  • Mutsuo Oka, Japan
  • Department of Mathematical Sciences
  • Centre for Quantum Geometry of Moduli Spaces
An irreducible non-torus plane sextic with simple singularities is said to be special if its fundamental group factors to a dihedral group. There exist (exactly) ten configurations of simple singularities that are realizable by such curves. Among them, six are realizable by non-special sextics as well. We conjecture that for each of these six configurations there always exists a non-special curve whose fundamental group is abelian, and we prove this conjecture for three configurations (another one has already been treated in one of our previous papers). As a corollary, we obtain new explicit examples of Alexander-equivalent Zariski pairs of irreducible sextics.
Original languageEnglish
JournalKodai Mathematical Journal
Volume32
Issue3
Pages (from-to)404-419
Number of pages16
ISSN0386-5991
DOIs
Publication statusPublished - 2009

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