CLASSICAL ZARISKI PAIRS


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Akyol A.

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, vol.21, no.9, 2012 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 21 Issue: 9
  • Publication Date: 2012
  • Doi Number: 10.1142/s0218216512500915
  • Title of Journal : JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS

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.