Integral representations of cyclic groups acting on relative holomorphic differentials of deformations of curves with automorphisms

TL;DR

This paper investigates how cyclic groups act on the space of holomorphic differentials during the deformation of algebraic curves, providing integral representations that enhance understanding of these symmetries.

Contribution

It introduces integral representations of holomorphic differentials for deformations of curves with cyclic automorphisms, advancing the understanding of group actions in algebraic geometry.

Findings

Derived explicit integral representations of group actions on differentials.

Analyzed the structure of deformations with cyclic automorphisms.

Enhanced understanding of automorphism group actions on curve deformations.

Abstract

We study integral representations of holomorphic differentials on the Oort-Sekiguci-Suwa component of deformations of curves with cyclic group actions.