The moduli space of totally marked degree two rational maps

Anupam Bhatnagar. "The moduli space of totally marked degree two rational maps." Acta Arithmetica 167.3 (2015): 251-260. <http://eudml.org/doc/279045>.

@article{AnupamBhatnagar2015,
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 $ 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].},
author = {Anupam Bhatnagar},
journal = {Acta Arithmetica},
keywords = {geometric invariant theory; moduli spaces; arithmetic dynamical systems},
language = {eng},
number = {3},
pages = {251-260},
title = {The moduli space of totally marked degree two rational maps},
url = {http://eudml.org/doc/279045},
volume = {167},
year = {2015},
}

TY - JOUR
AU - Anupam Bhatnagar
TI - The moduli space of totally marked degree two rational maps
JO - Acta Arithmetica
PY - 2015
VL - 167
IS - 3
SP - 251
EP - 260
AB - 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].
LA - eng
KW - geometric invariant theory; moduli spaces; arithmetic dynamical systems
UR - http://eudml.org/doc/279045
ER -