Cubic Polynomial Maps with Periodic Critical Orbit, Part II: Escape Regions

The parameter space $\mathcal{S}_p$ for monic centered cubic polynomial maps with a marked critical point of period $p$ is a smooth affine algebraic curve whose genus increases rapidly with $p$. Each $\mathcal{S}_p$ consists of a compact connectedness locus together with finitely many escape regions, each of which is biholomorphic to a punctured disk and is characterized by an essentially unique Puiseux series. This note will describe the topology of $\mathcal{S}_p$, and of its smooth compactification, in terms of these escape regions. It concludes with a discussion of the real sub-locus of $\mathcal{S}_p$.Comment: 51 pages, 16 figure

Un Ejemplo de la Compactificación de Deligne-Mumford.

Una introducción sencilla a los ejemplos más fáciles dela compactificación de Deligne-Mumford. (Con John Milnor)Non UBCUnreviewedAuthor affiliation: University of Rhode IslandFacult

Contractive curves

We discuss the dynamics of the correspondences associated to those plane curves whose local sections contract the Poincaré metric in a hyperbolic planar domain

Group actions, divisors, and plane curves

After a general discussion of group actions, orbifolds, and weak orbifolds, this note will provide elementary introductions to two basic moduli spaces over the real or complex numbers: first the moduli space of effective divisors with finite stabilizer on the projective space P1, modulo the group of projective transformations of P1; and then the moduli space of curves (or more generally effective algebraic 1-cycles) with finite stabilizer in P2, modulo the group of projective transformations of P2. It also discusses automorphisms of curves and the topological classification of smooth real curves in P2