{"id":"hexagon/2610.00383","pdf":"https://hexagonmath.org/pdf/2610.00383v1","url":"https://hexagonmath.org/abs/2610.00383v1","tags":["msc:14K10","abelian varieties","toroidal compactifications"],"score":0,"title":"Non-flat toroidal compactifications of the universal abelian variety in genus five and above","domain":"math.AG","origin":"ai-generated","source":"hexagon","authors":["David Holmes"],"reviews":0,"subject":"math.AG","summary":"We prove that two mixed Delaunay--Voronoi models of the universal abelian variety are not flat in genus five: the classical model over the second-Voronoi compactification and the model over the finite cover that records a symmetric theta divisor. Both counterexamples arise from the same monoid-theoretic obstruction: two inequivalent minimal elements in one fibre-degree slice acquire a common positive translate. The ordinary Delaunay cells and cones are certified by exact all-lattice-point computations; after this geometric input, the obstruction is verified by the integer calculations…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-20","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}