Indexed metadata

The geometry of solutions to the general sextic

Sidhanth Raman

Source record

Source: arXiv

Published: Sep 24, 2026

arXiv: 2609.30422

Open original source ↗

Source abstract

We study the geometry of the three simplest known formulas for roots of a general sextic polynomial. In contrast with work of Green on the quintic, we show that no "simultaneous uniformization" of the normal forms associated to the solutions exists. This demonstrates an intrinsic qualitative complexity of sextic equations that is not present in quintic equations. Additionally, we give a formula for the roots of a general sextic in terms of Hilbert modular cusp forms and the uniformizing differential equation of the associated Hilbert modular surface.

Evidence graph

No public relationships recorded yet.

Integrity note: This page is a factual metadata record created by deterministic ingestion. It is not a claim that the work moves a mathematical frontier or has been independently verified.

The geometry of solutions to the general sextic — Mathematical Frontier Network