TL;DR
This paper investigates the existence of Zariski partner sextics of non-torus type, providing a comprehensive list of their existence and non-existence based on previous classifications of torus type sextics with simple singularities.
Contribution
It offers a complete classification of Zariski partner sextics of non-torus type, expanding understanding of sextic curve configurations beyond torus types.
Findings
Complete list of existence and non-existence of Zariski partner sextics
Extension of previous classification of sextics with simple singularities
Clarification of relationships between torus and non-torus sextics
Abstract
The complete list of reducible sextics of torus type with simple singularities is known in our previous paper. In this paper, we give a complete list of existence and non-existence of Zariski partner sextics of non-torus type corresponding to the list of sextics of torus type.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Geometric and Algebraic Topology · Algebraic structures and combinatorial models