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University of Illinois – Chicago

1. Ye, Fei. Topology of Moduli Spaces and Complements of Hyperplane Arrangements.

Degree: 2011, University of Illinois – Chicago

URL: http://hdl.handle.net/10027/8044

A complex l-arrangement A is a finite collection of hyperplanes in a l-dimensional affine (or projective) space. The study of the interplay between the topology of the complement and combinatorial structure of an arrangement is one of the central topics in combinatorics, topology and algebraic geometry. My thesis aims to address the following natural questions:
1. When the combinatorial structure of a hyperplane arrangement will determine the topology of its complement?
2. To what extend the combinatorial structure of a fiber-type projective line arrangement will determine the topology of its complement?
3. When is the moduli space of line arrangements with fixed combinatorial structure connected?
I partially answer the first question by showing that if the arrangement A is nice or nice point then the moduli space is connected with respect to the fixed combinatorial structure of A. Fiber-type projective line arrangements are also studied towards the second question. I also find a counter example of two fiber-type projective line arrangements with same combinatorial structure but disconnected moduli space. However the fundamental groups of complements of the arrangements in the example are isomorphic. Toward to the third question, I classified arrangements of nine lines.
*Advisors/Committee Members: Yau, Stephen S. (advisor), Che, Chun-Tao (committee member), Ein, Lawrence M. (committee member), Popa, Mihnea (committee member), Marian, Alina (committee member).*

Subjects/Keywords: Moduli spaces; Hyperplane arrangements

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APA (6^{th} Edition):

Ye, F. (2011). Topology of Moduli Spaces and Complements of Hyperplane Arrangements. (Thesis). University of Illinois – Chicago. Retrieved from http://hdl.handle.net/10027/8044

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Ye, Fei. “Topology of Moduli Spaces and Complements of Hyperplane Arrangements.” 2011. Thesis, University of Illinois – Chicago. Accessed July 12, 2020. http://hdl.handle.net/10027/8044.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Ye, Fei. “Topology of Moduli Spaces and Complements of Hyperplane Arrangements.” 2011. Web. 12 Jul 2020.

Vancouver:

Ye F. Topology of Moduli Spaces and Complements of Hyperplane Arrangements. [Internet] [Thesis]. University of Illinois – Chicago; 2011. [cited 2020 Jul 12]. Available from: http://hdl.handle.net/10027/8044.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Ye F. Topology of Moduli Spaces and Complements of Hyperplane Arrangements. [Thesis]. University of Illinois – Chicago; 2011. Available from: http://hdl.handle.net/10027/8044

Not specified: Masters Thesis or Doctoral Dissertation