论文标题
在Yuzvinsky的晶格捆捆同学上，用于超平面布置
On Yuzvinsky's lattice sheaf cohomology for hyperplane arrangements
论文作者
论文摘要
我们在Yuzvinsky引入的超平面布置的交叉晶格上建立了一定捆的共同体之间的关系，与沿布置的对数矢量场模块相关的射击仿射空间的相干捆的共同体学分别在刺穿的仿射空间上。我们的主要结果给出了一个连接共同体理论的Künneth公式，并回答了Yoshinaga的问题。反过来，这提供了对数矢量场模块的投影维度的特征，并产生了Yuzvinsky的Freeness标准的新证明。此外，我们的方法提供了Terao FreeNess猜想和更普遍的问题的新表述。
We establish the relationship between the cohomology of a certain sheaf on the intersection lattice of a hyperplane arrangement introduced by Yuzvinsky and the cohomology of the coherent sheaf on punctured affine space, respectively projective space associated to the module of logarithmic vector fields along the arrangement. Our main result gives a Künneth formula connecting the cohomology theories, answering a question by Yoshinaga. This, in turn, provides a characterization of the projective dimension of the module of logarithmic vector fields and yields a new proof of Yuzvinsky's freeness criterion. Furthermore, our approach affords a new formulation of Terao's freeness conjecture and a more general problem.
