AI 中文总结
该研究刻画了丰富类完全交产生的莱夫谢茨算子的核，证明了相关混合莱夫谢茨性质、核的对角性质，建立了核解耦定理，并应用其证明了Shenfeld-van Handel与Hu-Xiao的猜想。
AI 中文摘要
我们研究由丰富类的完全交产生的莱夫谢茨算子的核。当这些类是半ample（半丰沛）时，我们对固定次数以下的混合莱夫谢茨性质给出完整刻画——所有障碍都由相关余维数的不可约子簇检测到。我们进一步证明，下一个次数范围内的核在对角外消失，而在对角上，它们的基由被莱夫谢茨算子零化的不可约子簇的基本类构成。我们还为复莱夫谢茨模上的丰富类建立了一个核解耦定理。作为应用，我们得到了超临界丰富类集合的核刻画，从而证明了Shenfeld-van Handel与Hu-Xiao的一个猜想。
英文摘要
We study the kernels of Lefschetz operators arising from complete intersections of nef classes. When the classes are semiample, we provide a complete characterization of mixed Lefschetz properties below a fixed degree -- all obstructions are detected by irreducible subvarieties of relevant codimensions. We further show that the kernels in the next degree range vanish off the diagonal, while on the diagonal they admit bases consisting of fundamental classes of irreducible subvarieties annihilated by the Lefschetz operator. We also establish a kernel decoupling theorem for nef classes on complex Lefschetz modules. As an application, we obtain a kernel characterization for supercritical collections of nef classes, thereby proving a conjecture of Shenfeld-van Handel and Hu-Xiao.
Comments45 pages, comments welcome!
