判别排列与Orlik-Solomon代数的上同调
On the cohomology of discriminantal arrangements and Orlik-Solomon algebras
摘要：
我们将判别式排列的Orlik-Solomon代数的上同调与补集的局部系统上同调联系起来。这种安排的Orlik-Solomon代数（视为一个复杂的）被证明是一个线性逼近的复所产生的基本群的补充，其上同调是同构的补充系数在一个任意复杂的秩一个本地系统。我们还建立了判别式排列的补集的上同调支持位点与其Orlik-Solomon代数的共振变种之间的关系。
英文摘要：
We relate the cohomology of the Orlik-Solomon algebra of a discriminantal arrangement to the local system cohomology of the complement. The Orlik-Solomon algebra of such an arrangement (viewed as a complex) is shown to be a linear approximation of a complex arising from the fundamental group of the complement, the cohomology of which is isomorphic to that of the complement with coefficients in an arbitrary complex rank one local system. We also establish the relationship between the cohomology support loci of the complement of a discriminantal arrangement and the resonant varieties of its Orlik-Solomon algebra.
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