Sean Monahan

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math.AG2024

Horospherical varieties with quotient singularities

Sean Monahan

Our main result is a combinatorial characterization of when a horospherical variety has (at worst) quotient singularities. Using this characterization, we show that every quasiproj…

math.AG2023

Approximating rational points on horospherical varieties

Sean Monahan, Matthew Satriano

Let $X$ be a smooth projective split horospherical variety over a number field $k$ and $x \in X (k)$ . Contingent on Vojta's conjecture, we construct a curve $C$ through $x$ such that…

math.AG2023

An overview of horospherical varieties and coloured fans

Sean Monahan

We provide an overview of the combinatorial theory of horospherical varieties using coloured fans, a generalization of the combinatorial theory of toric varieties using polyhedral…

math.AG2023

Horospherical stacks and stacky coloured fans

Sean Monahan

We introduce a combinatorial theory of horospherical stacks which is motivated by the work of Geraschenko and Satriano on toric stacks. A horospherical stack corresponds to a combi…