Theta characteristics and their moduli

TL;DR

This paper explores the geometry of theta characteristics, their moduli spaces, and connections to classical theta functions and string theory, providing a comprehensive overview of recent developments and historical context.

Contribution

It offers new insights into the birational geometry of spin moduli spaces and their parametrization through K3 surfaces, linking classical and modern theories.

Findings

Analysis of the birational geometry of spin moduli spaces

Parametrization of moduli via special K3 surfaces

Relations with classical theta function theory and superstring measures

Abstract

We discuss various aspects of the geometry of theta characteristics including the birational geometry of the spin moduli space of curves, parametrization of moduli via special K3 surfaces, as well as the relation with classical theta function theory and string theory in the form of the superstring measure. A historical view of the development of the subject is also presented.