Homological properties of determinantal arrangements

<p>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 × <em>n</em> 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.</p>

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Year

2016

Author dc:creator

• Yim, Arnold H

Contributors dc:contributor

• Hans U. Walther
• Donu Arapura
• Saugata Basu
• David B. McReynolds

• Pure sciences
• Determinantal arrangement
• Free divisor
• Hyperplane arrangement
• Mathematics

Repository record dc:identifier

https://docs.lib.purdue.edu/open_access_dissertations/731

OAI identifier oai:identifier

oai:docs.lib.purdue.edu:open_access_dissertations-1900