Moduli and periods of supersymmetric curves

Multiple Zeta Values and Periods of Moduli

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...

Compactifying Moduli of Hyperelliptic Curves

We construct a new compactification of the moduli space Hg of smooth hyperelliptic curves of genus g. We compare our compactification with other well-known remarkable compactifications of Hg.