Is there any way to tell from its defining equation when an affine hypersurface has a group law? I am aware that all such groups are matrix groups; in that case I might want to ask when a variety over $k$ admits a free and transitive action by an algebraic group over $k$? What necessary and sufficient conditions do we know of in low dimensions/arbitrary dimensions?
2026-03-25 17:45:00.1774460700
Abelian hypersurfaces
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