CLASSICAL ZARISKI PAIRS

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Akyol A.

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, vol.21, no.9, 2012 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 21 Issue: 9
  • Publication Date: 2012
  • Doi Number: 10.1142/s0218216512500915
  • Journal Name: JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Abdullah Gül University Affiliated: No

Abstract

We enumerate and classified up to equisingular deformation all irreducible plane sextics constituting the so called classical Zariski pairs. In most cases we obtain two deformation families, called abundant and non-abundant. Four sets of singularities are realized by abundant sextics only, and one exceptional set of singularities is realized by three families, one abundant and two complex conjugate non-abundant. This exceptional set of singularities has submaximal total Milnor number 18.

We enumerate and classify up to equisingular deformation all irreducible plane sextics constituting the so called classical Zariski pairs. In most cases we obtain two deformation families, called abundant and non-abundant. Four sets of singularities are realized by abundant sextics only, and one exceptional set of singularities is realized by three families, one abundant and two complex conjugate non-abundant. This exceptional set of singularities has submaximal total Milnor number 18.