Invariant Forms for Correspondences of Curves

TL;DR

This paper investigates invariant differential forms associated with correspondences of algebraic curves, aiming to classify those on the projective line that admit such forms, thereby advancing understanding of their structural properties.

Contribution

It introduces a classification of correspondences of  that admit invariant differential forms, providing new insights into their geometric and algebraic structure.

Findings

Classification of correspondences of  with invariant differential forms

Identification of conditions for the existence of invariant forms

Enhanced understanding of the structure of curve correspondences

Abstract

In this article, we study the invariant differential forms which a correspondence of curves admits. We also try to classify the correspondences of $\mathbb{P}^1$ that admits such invariant differential forms.