English

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

R2 v1 2026-06-21T15:55:15.985Z