The Moduli Space of Totally Marked Degree Two Rational Maps

2014/08/17 by Bhatnagar, Anupam
#14L30 #Algebraic Geometry (math.AG) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1408.3846

Abstract

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 of totally marked degree two rational maps, Rat^tm₂ can be parametrized by an affine open subset of (ℙ¹)⁵. We consider the natural action of SL₂ on Rat^tm₂ induced from the action of SL₂ on (ℙ¹)⁵ and prove that the quotient space Rat^tm₂/SL₂ exists as a scheme. The quotient is isomorphic to a Del Pezzo surface with the isomorphism being defined over ℤ[1/2].

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