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 can be parametrized by an affine open subset of (ℙ¹)⁵. We consider the natural action of SL₂ on induced from the action of SL₂ on (ℙ¹)⁵ and prove that the quotient space exists as a scheme. The quotient is isomorphic to a Del Pezzo surface with the isomorphism being defined over ℤ[1/2].
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa167-3-3,
author = {Anupam Bhatnagar},
title = {The moduli space of totally marked degree two rational maps},
journal = {Acta Arithmetica},
volume = {168},
year = {2015},
pages = {251-260},
zbl = {06414110},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa167-3-3}
}
Anupam Bhatnagar. The moduli space of totally marked degree two rational maps. Acta Arithmetica, Tome 168 (2015) pp. 251-260. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa167-3-3/