标题： 微分算子，各向异性，以及单纯球体 显示英文标题

标题： Differential operators, anisotropy, and simplicial spheres

摘要： 我们在任意正特征下的单纯球面的Stanley-Reisner环的通用Artinian约化中发现了涉及微分算子的恒等式。 这些恒等式推广了Papadakis和Petrotou用于证明代数g猜想的特征2恒等式。 我们利用这些恒等式来证明Stanley-Reisner环的通用Artinian约化上某些形式的非退化性，并证明弱Lefschetz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 use these identities to prove the anisotropy of certain forms on the generic artinian reduction of the Stanley-Reisner ring and to prove weak Lefschetz results.