Groups in Algebraic Geometry.

Uniformization by radicals

speaker: Gian Pietro Pirola (Università di Pavia)

abstract: Zariski proved the general complex projective curve of genus g>6 is not rationally uniformized by radicals, that is, admits no map to the projective line whose Galois group of the associated splitting field (i.e. the monodromy group) is solvable. We study the problem of curves algebraically uniformized by radicals, that is curves dominated by curves rationally uniformized by radicals. We give example of curves algebraically but not rationally uniformized by radicals.

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