Quartic rings associated to binary quartic forms

Melanie Matchett Wood

doi:10.1093/imrn/rnr070

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arXiv · 1007.5501

Quartic rings associated to binary quartic forms

Melanie Matchett Wood

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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.

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Melanie Matchett Wood. 2011-03-31. Quartic rings associated to binary quartic forms. https://doi.org/10.1093/imrn%2Frnr070

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