A moduli interpretation of untwisted binary cubic forms
Algebraic Geometry
2021-04-01 v1 Rings and Algebras
Abstract
We give a moduli interpretation to the quotient of (nondegenerate) binary cubic forms with respect to the natural -action on the variables. In particular, we show that these orbits are in bijection with pairs of -invariant elliptic curves together with -torsion Brauer classes that are invariant under complex multiplication. The binary cubic generic Clifford algebra plays a key role in the construction of this correspondence.
Cite
@article{arxiv.2103.16691,
title = {A moduli interpretation of untwisted binary cubic forms},
author = {Rajesh S. Kulkarni and Charlotte Ure},
journal= {arXiv preprint arXiv:2103.16691},
year = {2021}
}