Nonarchimedean Green functions and dynamics on projective space

Nonarchimedean Green Functions and Dynamics on Projective Space

Abstract. Let φ : PNK → P N K be a morphism of degree d ≥ 2 defined over a field K that is algebraically closed field and complete with respect to a nonarchimedean absolute value. We prove that a modified Green function ĝφ associated to φ is Hölder continuous on P (K) and that the Fatou set F(φ) of φ is equal to the set of points at which ĝΦ is locally constant. Further, ĝφ vanishes precisely o...

Monads on Projective Space

On the Photon Green Functions in Curved Space-time

Quantization of electrodynamics in curved space-time in the Lorenz gauge and with arbitrary gauge parameter makes it necessary to study Green functions of nonminimal operators with variable coefficients. Starting from the integral representation of photon Green functions, we link them to the evaluation of integrals involving Γ-functions. Eventually, the full asymptotic expansion of the Feynman ...

The Space of Morphisms on Projective Space

The theory of moduli of morphisms on P generalizes the study of rational maps on P1. This paper proves three results about the space of morphisms on P 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 Silverma...

Analytic Discs, Global Extremal Functions and Projective Hulls in Projective Space

Using a recent result of Lárusson and Poletsky regarding plurisubharmonic subextensions we prove a disc formula for the quasiplurisubharmonic global extremal function for domains in P. As a corollary we get a characterization of the projective hull for connected compact sets in P by the existence of analytic discs.