Date of Award
5-2016
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematics
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
Abstract
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.
Recommended Citation
Yim, Arnold H., "Homological properties of determinantal arrangements" (2016). Open Access Dissertations. 731.
https://docs.lib.purdue.edu/open_access_dissertations/731