The field of definition for dynamical systems on P^N

2013/09/26 by Benjamin Hutz, Hutz, Benjamin, Michelle Manes +1
Mathematics · #11G99 (secondary) #37P45 (primary) #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11G99 #msc:37P45

paper · pdf · doi:10.48550/arxiv.1309.6696

arxiv created 2013/09/26 · arxiv updated 2013/09/27

Abstract

Let Hom^N_d be the set of morphisms of degree d from P^N to itself. For f an element of PGL_N+1, let phi^f represent the conjugation action f^-1 phi f. Let M^N_d = Hom_d^N/PGL_N+1 be the moduli space of degree d morphisms of P^N. A field of definition for class of morphisms is a field over which at least one morphism in the class is defined. The field of moduli for a class of morphisms is the fixed field of the set of Galois elements fixing that class. Every field of definition contains the field of moduli. In this article, we give a sufficient condition for the field of moduli to be a field of definition for morphisms whose stabilizer group is trivial.

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