Graduation Year
2024
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Science
Department
Mathematics
Reader 1
Dagan Karp
Reader 2
Siddarth Kannan
Terms of Use & License Information
Abstract
Moduli spaces provide a useful method for studying families of mathematical objects. We study certain moduli spaces of algebraic curves, which are generalizations of familiar lines and conics. This thesis focuses on, Δ(r,n), the dual boundary complex of the moduli space of genus-zero cyclic curves. This complex is itself a moduli space of graphs and can be investigated with combinatorial methods. Remarkably, the combinatorics of this complex provides insight into the geometry and topology of the original moduli space. In this thesis, we investigate two topologically invariant properties of Δ(r,n). We compute its Euler characteristic and we provide a conjecture and multiple possible proof techniques for calculating its homotopy type. Finally, we briefly discuss additional questions that might provide interesting future investigation of this complex.
Recommended Citation
Anderson, Toby, "The Dual Boundary Complex of the Moduli Space of Cyclic Compactifications" (2024). HMC Senior Theses. 284.
https://scholarship.claremont.edu/hmc_theses/284
Included in
Algebraic Geometry Commons, Discrete Mathematics and Combinatorics Commons, Geometry and Topology Commons
