Graduation Year
2012
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Science
Department
Mathematics
Reader 1
Dagan Karp
Reader 2
Davesh Maulik
Terms of Use & License Information
This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.
Rights Information
© Dhruv Ranganathan
Abstract
We use toric symmetry and blowups to study relationships in the Gromov-Witten theories of $\mathbb{P}^3$ and $\mathbb{P}^1\!\times\!\mathbb{P}^1\!\times\!\mathbb{P}^1$. These two spaces are birationally equivalent via the common blowup space, the permutohedral variety. We prove an equivalence of certain invariants on blowups at only points of $\mathbb{P}^3$ and $\mathbb{P}^1\!\times\!\mathbb{P}^1\!\times\!\mathbb{P}^1$ by showing that these invariants descend from the blowup. Further, the permutohedral variety has nontrivial automorphisms of its cohomology coming from toric symmetry. These symmetries can be forced to descend to the blowups at just points of $\mathbb{P}^3$ and $\mathbb{P}^1\!\times\!\mathbb{P}^1\!\times\!\mathbb{P}^1$. Enumerative consequences are discussed.
Recommended Citation
Ranganathan, Dhruv, "Gromov-Witten Theory of Blowups of Toric Threefolds" (2012). HMC Senior Theses. 31.
https://scholarship.claremont.edu/hmc_theses/31
