arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 0905.1284math.AG
收藏

超平面构形的第一Milnor上同调

First Milnor cohomology of hyperplane arrangements

Nero Budur, Alexandru Dimca, Morihiko Saito

摘要:

给出了满足一定组合条件的超平面排列的第一Milnor上同调的非幂幺单值部分维数的下界的组合公式。如果满足一个更强的组合条件,这正好给出了它的维数。我们还证明了一个非组合公式的第一Milnor上同调,这显然取决于奇点的位置的非幂幺部分的尺寸。后者推广了第二个命名的作者以前获得的公式。

英文摘要:

We show a combinatorial formula for a lower bound of the dimension of the non-unipotent monodromy part of the first Milnor cohomology of a hyperplane arrangement satisfying some combinatorial conditions. This gives exactly its dimension if a stronger combinatorial condition is satisfied. We also prove a non-combinatorial formula for the dimension of the non-unipotent part of the first Milnor cohomology, which apparently depends on the position of the singular points. The latter generalizes a formula previously obtained by the second named author.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑