The Space of Morphisms on Projective Space
By Alon Y. Levy. 2009
59 citations recorded by the source corpus.
The theory of moduli of morphisms on P^n generalizes the study of rational maps on P^1. This paper proves three results about the space of morphisms on P^n of degree d > 1, and its quotient by the conjugation action of PGL(n+1). First, we prove that this quotient is geometric, and compute the stable and semistable completions of the space of morphisms. This strengthens previous results of Silverman, as well as of Petsche, Szpiro, and Tepper. Second, we bound the size of the stabilizer group in PGL(n+1) of every morphism in terms of only n and d. Third, we specialize to the case where n = 1, and show that the quotient space is rational for all d > 1; this partly generalizes a result of Silverman about the case d = 2.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/350eee432c2592a351018867c2412d884df144f9
How researchers see this paper
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In Geometry and Topology
- T. Tucker
- Robert L. Benedetto
- Laura Demarco
- Joseph H. Silverman
- Michelle Manes
- Rafe Jones
- Patrick Ingram
- Franccois Berteloot
In Mathematical Physics
- T. Tucker
- Robert L. Benedetto
- Michelle Manes
- Rafe Jones
- Laura Demarco
- Patrick Ingram
- Joseph H. Silverman
- Franccois Berteloot
Citations in the corpus
- Current trends and open problems in arithmetic dynamics (2018, background): “(b) (Silverman [213]; Petsche–Szpiro–Tepper [189]; Levy [150]) MNd exists as a geometric quotient scheme over Spec(Z) in the sense of geometric invariant theory (GIT ).”