English

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 GL2\text{GL}_2-action on the variables. In particular, we show that these GL2\text{GL}_2 orbits are in bijection with pairs of jj-invariant 00 elliptic curves together with 33-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.

Keywords

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}
}
R2 v1 2026-06-24T00:42:46.279Z