Abstract:We calculate the determinant of the bilinear form in middle degree of the generic artinian reduction of the Stanley-Reisner ring of an odd-dimensional simplicial sphere. This proves the odd multiplicity conjecture of Papadakis and Petrotou and implies that this determinant is a complete invariant of the simplicial sphere. We extend this result to odd-dimensional connected oriented simplicial homology manifolds. In characteristic 2, we prove a generalization to the Hodge-Riemann forms of any connected simplicial homology manifold. To prove the latter theorem we establish the strong Lefschetz property for certain quotients of the Stanley-Reisner rings of connected simplicial pseudomanifolds.
From: Matt Larson [view email]
[v1]
Mon, 5 Aug 2024 18:00:10 UTC (20 KB)
[v2]
Wed, 14 Aug 2024 04:30:19 UTC (21 KB)
[v3]
Fri, 13 Sep 2024 16:00:32 UTC (28 KB)
[v4]
Fri, 7 Aug 2026 13:48:54 UTC (29 KB)
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