The moduli space of totally marked degree two rational maps

• Autorzy: Anupam Bhatnagar
• Języki publikacji: EN

Abstrakty

EN

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].

Kategorie tematyczne

• 14L24: Geometric invariant theory
• 14L30: Group actions on varieties or schemes (quotients)
• 37P45: Families and moduli spaces
• 14D22: Fine and coarse moduli spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2015
• Tom: 167
• Numer: 3
• Strony: 251-260

Daty

wydano

2015

Twórcy

autor

Anupam Bhatnagar

• Department of Mathematics, Borough of Manhattan Community College, The City University of New York, 199 Chambers Street, New York, NY 10007, U.S.A.

Identyfikatory

DOI

10.4064/aa167-3-3