Klein's Fundamental 2-Form of Second Kind for the $C_{ab}$ Curves
Algebraic Geometry
2017-03-20 v2
Abstract
In this paper, we derive the exact formula of Klein's fundamental 2-form of second kind for the so-called curves. The problem was initially solved by Klein in the 19th century for the hyper-elliptic curves, but little progress had been seen for its extension for more than 100 years. Recently, it has been addressed by several authors, and was solved for subclasses of the curves whereas they found a way to find its individual solution numerically. The formula gives a standard cohomological basis for the curves, and has many applications in algebraic geometry, physics, and applied mathematics, not just analyzing sigma functions in a general way.
Keywords
Cite
@article{arxiv.1701.00931,
title = {Klein's Fundamental 2-Form of Second Kind for the $C_{ab}$ Curves},
author = {Joe Suzuki},
journal= {arXiv preprint arXiv:1701.00931},
year = {2017}
}