Quartic rings associated to binary quartic forms
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- July 2010
- DOI:
- 10.48550/arXiv.1007.5501
- arXiv:
- arXiv:1007.5501
- Bibcode:
- 2010arXiv1007.5501M
- Keywords:
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- Mathematics - Number Theory;
- Mathematics - Algebraic Geometry;
- 11R04;
- 11E76
- E-Print:
- to appear in IMRN, section on geometric analogs over an arbitrary base added since version 1