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• W4210341036 abstract "We consider conformal actions of the finite group<inline-formula content-type=math/mathml><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper G><mml:semantics><mml:mi>G</mml:mi><mml:annotation encoding=application/x-tex>G</mml:annotation></mml:semantics></mml:math></inline-formula>on a closed Riemann surface<inline-formula content-type=math/mathml><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper S><mml:semantics><mml:mi>S</mml:mi><mml:annotation encoding=application/x-tex>S</mml:annotation></mml:semantics></mml:math></inline-formula>, as well as algebraic actions of<inline-formula content-type=math/mathml><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper G><mml:semantics><mml:mi>G</mml:mi><mml:annotation encoding=application/x-tex>G</mml:annotation></mml:semantics></mml:math></inline-formula>on smooth, complete, algebraic curves over an arbitrary, algebraically closed field. There are several notions of equivalence of actions, the most studied of which is topological equivalence, because of its close relationship to the branch locus of moduli space. A second important equivalence relation is that induced by representation of<inline-formula content-type=math/mathml><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper G><mml:semantics><mml:mi>G</mml:mi><mml:annotation encoding=application/x-tex>G</mml:annotation></mml:semantics></mml:math></inline-formula>on spaces of holomorphic<inline-formula content-type=math/mathml><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=q><mml:semantics><mml:mi>q</mml:mi><mml:annotation encoding=application/x-tex>q</mml:annotation></mml:semantics></mml:math></inline-formula>-differentials. The notion of topological equivalence does not work well in positive characteristic. We shall discuss an alternative to topological equivalence, which we dub equisymmetry, that may be applied in all characteristics. The relation is induced by families of curves with<inline-formula content-type=math/mathml><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper G><mml:semantics><mml:mi>G</mml:mi><mml:annotation encoding=application/x-tex>G</mml:annotation></mml:semantics></mml:math></inline-formula>-action, and it works well with rotation constants and<inline-formula content-type=math/mathml><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=q><mml:semantics><mml:mi>q</mml:mi><mml:annotation encoding=application/x-tex>q</mml:annotation></mml:semantics></mml:math></inline-formula>-differentials, which are also defined in positive characteristic. After giving an overview of the various equivalence relations (conformal/algebraic, topological,<inline-formula content-type=math/mathml><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=q><mml:semantics><mml:mi>q</mml:mi><mml:annotation encoding=application/x-tex>q</mml:annotation></mml:semantics></mml:math></inline-formula>-differentials, rotation constants, equisymmetry) we focus on the interconnections among rotation constants,<inline-formula content-type=math/mathml><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=q><mml:semantics><mml:mi>q</mml:mi><mml:annotation encoding=application/x-tex>q</mml:annotation></mml:semantics></mml:math></inline-formula>-differentials, and equisymmetry." @default.
• W4210341036 created "2022-02-08" @default.
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• W4210341036 date "2022-01-01" @default.
• W4210341036 modified "2023-09-29" @default.
• W4210341036 title "Equivalence of finite group actions on Riemann surfaces and algebraic curves" @default.
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• W4210341036 doi "https://doi.org/10.1090/conm/776/15609" @default.
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