Quartic rings associated to binary quartic forms
Number Theory
2011-05-03 v2 Algebraic Geometry
Abstract
We give a bijection between binary quartic forms and quartic rings with a monogenic cubic resolvent ring, relating the rings associated to binary quartic forms with Bhargava's cubic resolvent rings. This gives a parametrization of quartic rings with monogenic cubic resolvents. We also give a geometric interpretation of this parametrization.
Cite
@article{arxiv.1007.5501,
title = {Quartic rings associated to binary quartic forms},
author = {Melanie Matchett Wood},
journal= {arXiv preprint arXiv:1007.5501},
year = {2011}
}
Comments
to appear in IMRN, section on geometric analogs over an arbitrary base added since version 1