New and General Type Meromorphic $1$-forms on Curves
Abstract
In this article, we study the existence of new and general type meromorphic $1$-forms on curves through explicit construction. Specifically, we have constructed a large family of new and general type meromorphic $1$-forms on $\mathbb{P}^1,$ 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 $1$-form on $\mathbb{P}^1$ (of some restricted class) is new or old.
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2024
- DOI:
- 10.48550/arXiv.2408.00302
- arXiv:
- arXiv:2408.00302
- Bibcode:
- 2024arXiv240800302K
- Keywords:
-
- Mathematics - Algebraic Geometry;
- 12H05;
- 14H99;
- 34A26
- E-Print:
- 17 pages