Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)



First Advisor

Hans U. Walther

Committee Chair

Hans U. Walther

Committee Member 1

Donu Arapura

Committee Member 2

Saugata Basu

Committee Member 3

David B. McReynolds


We study a certain family of hypersurface arrangements known as determinantal arrangements. Determinantal arrangements are a union of varieties defined by minors of a matrix of indeterminates. In particular, we investigate determinantal arrangements using the 2-minors of a 2 × n generic matrix (which can be thought of as natural extensions of braid arrangements), and prove certain statements about their freeness. We also study the topology of these objects. We construct a fibration for the complement of free determinantal arrangements, and use this fibration to prove statements about their homotopy groups. Furthermore, we show that the Poincaré polynomial of the complement factors nicely.

Included in

Mathematics Commons