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Anisotropy, biased pairings, and the Lefschetz property for pseudomanifolds and cycles
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We prove the hard Lefschetz property for pseudomanifolds and cycles in any characteristic with respect to an appropriate Artinian reduction. The proof is a combination of Adiprasito's biased pairing theory and a generalization of a formula of Papadakis-Petrotou to arbitrary characteristic. In particular, we prove the Lefschetz theorem for doubly Cohen Macaulay complexes, solving a generalization of the g-conjecture due to Stanley. We also provide a simplified presentation of the characteristic 2 case, and generalize it to pseudomanifolds and cycles.
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Cited by 1 Pith paper
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On the weak and strong Lefschetz properties for initial ideals of determinantal ideals with respect to diagonal monomial orders
For initial ideals of determinantal ideals with respect to diagonal monomial orders, the author proves SLP for maximal minors and WLP failure for non-maximal minors when mn is large enough.
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