# Takuro, Abe:COE Research Fellow,Algebra

- Keyword(s):
- vector bundle, hyperplane arrangement, logarithmic vector field
- Research Interest:
- Algebraic Geometry, Hyperplane arrangement
- Research Activities:
- There are only few results known in the study of non-splitting vector bundles of lower rank on projectives spaces. In particular, almost nothing is known on those on four dimensional projective spaces. Through the elementary transformation or splitting criterion of vector bundles, I study the property and looking for the explicit construction of vector bundles. Moreover, recently, I also study the hyperplane arrangements, its combinatorics and the logarithmic vector fields, which is a reflexive sheaf on a projective space, associated to arrangements.
So my interest and the aim of these studies is, the Hartshorne conjecture on the splitting of vector bundles on projective spaces, and the Terao conjecture on the freeness and combinatorics of hyperplane arrangements.