Jordan curves with polynomial inverse moduli of continuity

Moduli of Continuity

Homeomorphisms of Jordan Curves

The notation and terminology used in this paper are introduced in the following articles: [20], [21], [1], [3], [22], [4], [5], [19], [10], [18], [7], [17], [11], [2], [8], [9], [16], [13], [14], [15], [6], [23], and [12]. In this paper p1, p2 are points of E 2 T, C is a simple closed curve, and P is a subset of E T. Let n be a natural number, let A be a subset of En T, and let a, b be points o...

Moduli of Elliptic Curves

The purpose of these notes is to provide a quick introduction to the moduli of elliptic curves. There are many excellent and thorough references on the subject, ranging from the slightly archaic [Igu59] and [Shi94] to the more difficult [KM85] and [DR73]. Brian’s forthcoming book on the Ramanujan conjecture also covers some of this material and includes a careful comparison of the transcendenta...

Singular Moduli of Shimura Curves

The j-function acts as a parametrization of the classical modular curve. Its values at complex multiplication (CM) points are called singular moduli and are algebraic integers. A Shimura curve is a generalization of the modular curve and, if the Shimura curve has genus 0, a rational parameterizing function exists and when evaluated at a CM point is again algebraic over Q. This paper shows that ...

Moduli of Twisted Spin Curves

In this note we give a new, natural construction of a compactification of the stack of smooth r-spin curves, which we call the stack of stable twisted r-spin curves. This stack is identified with a special case of a stack of twisted stable maps of Abramovich and Vistoli. Realizations in terms of admissible Gm-spaces and Q-line bundles are given as well. The infinitesimal structure of this stack...