New and General Type Meromorphic $1$-forms on Curves
Algebraic Geometry
2025-09-23 v2
Abstract
In this article, we study the existence of new and general type meromorphic -forms on curves through explicit construction. Specifically, we have constructed a large family of new and general type meromorphic -forms on elliptic and hyperelliptic curves. We also established a connection to the Hurwitz realization problem of branch cover for the Riemann Sphere, which provides an algorithm to determine whether a -form on (of some restricted class) is new or old.
Keywords
Cite
@article{arxiv.2408.00302,
title = {New and General Type Meromorphic $1$-forms on Curves},
author = {Partha Kumbhakar},
journal= {arXiv preprint arXiv:2408.00302},
year = {2025}
}
Comments
This version replaces the previous one, with minor revisions. Accepted for publication in Communications in Algebra (18 pages)