有限射影平面的代数方法
An algebraic approach to finite projective planes
摘要：
一个有限的射影平面，或者更一般地说一个有限的线性空间，有一个相关的关联复形，它产生了两个自然代数：斯坦利-赖斯纳环$R/I_Λ$和逆系统代数$R/I_Δ$。我们仔细研究这两个代数。我们的主要结果是一个完整的描述的分次贝蒂数的代数在更一般的设置的线性空间（给出的结果作为特殊情况下的射影平面），和分类的特征，其中逆系统代数与有限的射影平面有弱或强Lefschetz性质。
英文摘要：
A finite projective plane, or more generally a finite linear space, has an associated incidence complex that gives rise to two natural algebras: the Stanley-Reisner ring $R/I_Λ$ and the inverse system algebra $R/I_Δ$. We give a careful study of both of these algebras. Our main results are a full description of the graded Betti numbers of both algebras in the more general setting of linear spaces (giving the result for the projective planes as a special case), and a classification of the characteristics in which the inverse system algebra associated to a finite projective plane has the Weak or Strong Lefschetz Property.
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