Spin Structures and Branch Divisors on $p$-gonal Riemann surfaces

TL;DR

This paper investigates spin structures on p-gonal Riemann surfaces, focusing on divisors supported on branch points and their invariance under surface automorphisms and involutions.

Contribution

It provides a detailed analysis of spin structures on hyperelliptic and p-gonal surfaces using divisor theory, including invariance properties under symmetries.

Findings

Characterization of spin structures via branch point divisors

Analysis of invariant spin divisors under automorphisms

Insights into spin structures on hyperelliptic and p-gonal surfaces

Abstract

We study spin structures on Riemann and Klein surfaces in terms of divisors. In particular, we take a closer look at spin structures on hyperelliptic and $p$-gonal surfaces defined by divisors supported on their branch points. Moreover, we study invariant spin divisors under automorphisms and anti-holomorphic involutions of Riemann surfaces.