• Corpus ID: 232427866

# A moduli interpretation of untwisted binary cubic forms

@inproceedings{Kulkarni2021AMI,
title={A moduli interpretation of untwisted binary cubic forms},
author={Rajesh S. Kulkarni and Charlotte Ure},
year={2021}
}
• Published 30 March 2021
• Mathematics
We give a moduli interpretation to the quotient of (nondegenerate) binary cubic forms with respect to the natural GL2-action on the variables. In particular, we show that these GL2 orbits are in bijection with pairs of j-invariant 0 elliptic curves together with 3-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. Introduction The subject of homogeneous forms has…
1 Citations
. We consider the question of determining whether two binary cubic forms over an arbitrary ﬁeld K whose characteristic is not 2 or 3 are equivalent under the actions of either GL(2 ,K ) or SL(2 ,K ),

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