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The moduli space of totally marked degree two rational maps

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Bhatnagar A.

Acta Arithmetica

2015

tom 167

nr 3

251-260

A rational map ϕ: ℙ¹ → ℙ¹ along with an ordered list of fixed and critical points is called a totally marked rational map. The space $ Rat₂^tm$ of totally marked degree two rational maps can be parametrized by an affine open subset of (ℙ¹)⁵. We consider the natural action of SL₂ on $ Rat₂^tm$ induced from the action of SL₂ on (ℙ¹)⁵ and prove that the quotient space $Rat₂^tm/SL₂$ exists as a scheme. The quotient is isomorphic to a Del Pezzo surface with the isomorphism being defined over ℤ[1/2].

Ograniczanie wyników

1 Acta Arithmetica

1 Bhatnagar A.

1 2015

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The moduli space of totally marked degree two rational maps