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Oka's conjecture on irreducible plane sextics
Author(s) -
Degtyarev Alex
Publication year - 2008
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdn029
Subject(s) - mathematics , conjecture , gravitational singularity , plane (geometry) , pure mathematics , simple (philosophy) , dihedral group , algebra over a field , combinatorics , group (periodic table) , geometry , mathematical analysis , physics , philosophy , epistemology , quantum mechanics
We partially prove and partially disprove Oka's conjecture on the fundamental group/Alexander polynomial of an irreducible plane sextic. Among other results, we enumerate all irreducible sextics with simple singularities admitting dihedral coverings and find examples of Alexander equivalent Zariski pairs of irreducible sextics.