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Solving the sextic by iteration: a study in complex geometry and dynamics. (English) Zbl 1060.14530

Summary: We use the Valentiner action of the alternating group \(A_6\) on \(\mathbb C\mathbb P^2\) to develop an iterative algorithm for the solution of the general sextic equation over \(\mathbb C\), analogous to Doyle and McMullen’s algorithm for the quintic [see P. G. Doyle and C. T. McMullen, Acta Math. 163, No. 3-4, 151–180 (1989; Zbl 0705.65036)].

MSC:

14N99 Projective and enumerative algebraic geometry
14H45 Special algebraic curves and curves of low genus
14L30 Group actions on varieties or schemes (quotients)
37F10 Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets
37F50 Small divisors, rotation domains and linearization in holomorphic dynamics

Citations:

Zbl 0705.65036
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References:

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[2] DOI: 10.1017/CBO9780511565809 · doi:10.1017/CBO9780511565809
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