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arXiv · 2408.00302

New and General Type Meromorphic $1$-forms on Curves

Partha Kumbhakar
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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.

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Partha Kumbhakar. 2024-08-01. New and General Type Meromorphic $1$-forms on Curves. https://arxiv.org/abs/2408.00302

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