标题： 微分算子，各向异性，和单纯球面 显示英文标题

标题： Differential operators, anisotropy, and simplicial spheres

摘要： 我们发现在单纯球的Stanley-Reisner环在任意正特征下的generic artinian约化中，涉及微分算子的一些恒等式。 这些恒等式推广了Papadakis和Petrotou在特征2下使用的恒等式，用以证明代数g-猜想。 我们证明这些恒等式是关于次数映射的一个恒等式的影子，并利用它们来证明Stanley-Reisner环的generic artinian约化中某些形式的各向异性，以及证明弱Lefschetz性质的结果。 显示英文摘要

摘要： We find identities involving differential operators in the generic artinian reduction of the Stanley-Reisner ring of a simplicial sphere in any positive characteristic. These identities generalize the characteristic 2 identities used by Papadakis and Petrotou to give a proof of the algebraic g-conjecture. We show that these identities are a shadow of an identity on the degree map, and we use them to prove the anisotropy of certain forms on the generic artinian reduction of the Stanley--Reisner ring and to prove weak Lefschetz results.