Determinants of Hodge-Riemann forms
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909314294218752 |
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| author | Larson, Matt Novik, Isabella Stapledon, Alan |
| author_facet | Larson, Matt Novik, Isabella Stapledon, Alan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_02737 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Determinants of Hodge-Riemann forms Larson, Matt Novik, Isabella Stapledon, Alan Commutative Algebra Combinatorics 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. |
| title | Determinants of Hodge-Riemann forms |
| topic | Commutative Algebra Combinatorics |
| url | https://arxiv.org/abs/2408.02737 |