Department of Mathematics - Seminar on Pure Mathematics - Extension and combinatorial configurations of hyperplane arrangements

We examine three types of extensions of hyperplane arrangements: elementary lift, parallel translation and adding a new hyperplane arbitrarily. The configuration spaces of elementary lift, parallel translation, and adding a new hyperplane are parametrized by continuous multi-variables. We classify the combinatorial types (finitely many) of the configuration spaces of the hyperplane arrangements for each of the three extensions and characterize their intersection lattices. Furthermore, we also describe the order-preserving relations on various combinatorial invariants of the extended hyperplane arrangements.