Geometry and combinatorics of hyperplane arrangements

在第一年，我研究了对数向量场的层与因子的射影空间。我得到了一般超曲面的Torelli型定理的几个结果（与K.上田）和多重性超平面排列的自由度。在第二年和第三年，我研究了超平面排列的极小性及其应用。我得到了基本群的新表述和扭曲上同调群消失的一个刻画。

In the first year, I studied the sheaf of logarithmic vector fields associated to divisors on the projective space. I obtained several results on Torelli-type theorem for generic hypersurface (Collaboration with K. Ueda) and on the freeness for hyperplane arrangements with multiplicities. In the second and third year, I studied minimality of hyperplane arrangements and applications. I obtained new presentations for fundamental groups and a characterization for vanishing twisted cohomology groups.