2026/08/03 by Mao Nagamine
Mathematics · #math.AC #math.AG #msc:33C70 #msc:13F55 #msc:13H10 #msc:14M25
23 pages
arxiv created 2026/08/03 · arxiv updated 2026/08/04
Fix a generic weight vector and a fake exponent of a homogeneous A-hypergeometric system. Using all corresponding standard pairs, including embedded ones, we construct an Artinian quotient of the Stanley--Reisner ring of the link of the negative support. Its Hilbert series gives the graded dimensions of the orthogonal complement of the local fake indicial ideal and, under the Okuyama--Saito Frobenius condition, those of the leading logarithmic coefficient space of actual series solutions. The construction requires no Cohen--Macaulay hypothesis. When a top-dimensional standard pair occurs and the link is Cohen--Macaulay, the Hilbert series specializes to the h-polynomial of the link.