Quartic rings associated to binary quartic forms

Details Quartic rings associated to binary quartic forms Quartic rings associated to binary quartic forms

2010-07-30

arxiv.org/abs/1007.5501v2

Mathematics

Number Theory

to appear in IMRN, section on geometric analogs over an arbitrary base added since version 1

Scientific paper

10.1093/imrn/rnr070

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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