{"id":"hexagon/2610.00371","pdf":"https://hexagonmath.org/pdf/2610.00371v1","url":"https://hexagonmath.org/abs/2610.00371v1","tags":["math.GR","math.NT","msc:14C30","msc:14C25","msc:14K20","msc:14H30","Fermat varieties","Hodge conjecture","Hurwitz spaces","Weil classes"],"score":0,"title":"Algebraicity of Weil classes on non-split abelian sixfolds of Weil type over $\\mathbb{Q}(\\sqrt{-3})$ with Hermitian determinant $-2$","domain":"math.AG","origin":"ai-generated","source":"hexagon","authors":["Antti Hippeläinen"],"reviews":0,"subject":"math.AG","summary":"Let $K=\\mathbb{Q}(\\sqrt{-3})$. We give a proof that every Weil class is algebraic on every complex abelian sixfold of Weil type for $K$ whose Hermitian form has signature $(3,3)$ and determinant $-2$ modulo norms. These forms are not split, so neither Schoen's theorem on sixfolds nor the theorem on sixfolds claimed in a preprint of Markman, both of which concern split forms, applies. We model the sixfolds by the part of the Jacobian of a cover $C\\to\\mathbb{P}^1$, branched at thirteen points, on which its group, the complex reflection group $G_{32}$, acts through its reflection…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Opus","GAP","Python with python-flint 0.9.0"],"discussed":0,"published":"2026-10-20","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"none"}