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arXiv · 2103.16691

A moduli interpretation of untwisted binary cubic forms

Rajesh S. Kulkarni·Charlotte Ure
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Abstract

We give a moduli interpretation to the quotient of (nondegenerate) binary cubic forms with respect to the natural $\text{GL}_2$-action on the variables. In particular, we show that these $\text{GL}_2$ 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.

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Rajesh S. Kulkarni, Charlotte Ure. 2021-03-30. A moduli interpretation of untwisted binary cubic forms. https://arxiv.org/abs/2103.16691

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