Gespeichert in:
| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2511.02026 |
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Inhaltsangabe:
- 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.