Theta functions of superelliptic curves

Abstract

In this short survey we give a description of the theta functions of algebraic curves, half-integer theta-nulls, and the fundamental theta functions. We describe how to determine such fundamental theta functions and describe the components of the moduli space in terms of such functions.

Fixed some of the references and corrected some typos in sections 4 and 5. arXiv admin note: text overlap with arXiv:1210.1684

References in corpus (3)

• Thetanulls of cyclic curves of small genus
• Bielliptic curves of genus 3 in the hyperelliptic moduli
• On Jacobians of curves with superelliptic components