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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2511.02026 |
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| _version_ | 1866917057820360704 |
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| author | Amini, Omid Huh, June Larson, Matt |
| author_facet | Amini, Omid Huh, June Larson, Matt |
| contents | A Lefschetz module is a module over a graded algebra $A$ that satisfies analogues of Poincaré duality, the Hard Lefschetz property, and the Hodge--Riemann relations with respect to an open convex cone $\mathscr{K}$ in the degree one part of $A$. We analyze its decomposition into indecomposable modules over subrings of $A$ that are generated by elements in the closure of $\mathscr{K}$, establishing structural results that parallel the decomposition theorem for morphisms of complex projective varieties. We use our theorems to recover key statements in combinatorial Hodge theory and illuminate the Hodge-theoretic aspects of the decomposition theorem in algebraic geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_02026 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A decomposition theorem for Lefschetz modules Amini, Omid Huh, June Larson, Matt Algebraic Geometry Combinatorics A Lefschetz module is a module over a graded algebra $A$ that satisfies analogues of Poincaré duality, the Hard Lefschetz property, and the Hodge--Riemann relations with respect to an open convex cone $\mathscr{K}$ in the degree one part of $A$. We analyze its decomposition into indecomposable modules over subrings of $A$ that are generated by elements in the closure of $\mathscr{K}$, establishing structural results that parallel the decomposition theorem for morphisms of complex projective varieties. We use our theorems to recover key statements in combinatorial Hodge theory and illuminate the Hodge-theoretic aspects of the decomposition theorem in algebraic geometry. |
| title | A decomposition theorem for Lefschetz modules |
| topic | Algebraic Geometry Combinatorics |
| url | https://arxiv.org/abs/2511.02026 |