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Olivia Beckwith


On Toric Symmetry of $\mathbb{P}^1 \times \mathbb{P}^2$

Dagan Karp
Second Reader(s)
Dusty Ross


Toric varieties are a class of geometric objects with a combinatorial structure encoded in polytopes. $\mathbb{P}^1 \times \mathbb{P}^2$ is a well known variety and its polytope is the triangular prism. Studying the symmetries of the triangular prism and its truncations can lead to symmetries of the variety. Many of these symmetries permute the elements of the cohomology ring nontrivially and induce nontrivial relations. We discuss some toric symmetries of $\mathbb{P}^1 \times \mathbb{P}^2$, and describe the geometry of the polytope of the corresponding blowups, and analyze the induced action on the cohomology ring. We exhaustively compute the toric symmetries of $\mathbb{P}^1 \times \mathbb{P}^2$.

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