Tonie Scroggin

activity

20232025

collaborators

4 papers

math.AG2025

Splicing braid varieties

Eugene Gorsky, Soyeon Kim, Tonie Scroggin +1

For a positive braid $β \in Br_{k}^{+}$ , we consider the braid variety $X (β)$ . We define a family of open sets $U_{r, w}$ in $X (β)$ , where $w \in S_{k}$ is a permut…

math.AG2025

Splicing skew shaped positroids

Eugene Gorsky, Soyeon Kim, Tonie Scroggin +1

Skew shaped positroids (or skew shaped positroid varieties) are certain Richardson varieties in the flag variety that admit a realization as explicit subvarieties of the Grassmanni…

math.AG2024

Splicing positroid varieties

Eugene Gorsky, Tonie Scroggin

We construct an explicit isomorphism between an open subset in the open positroid variety $Π_{k, n}^{\circ}$ in the Grassmannian $Gr (k, n)$ and the product of two open posit…

math.AG2023

On the Cohomology of Two Stranded Braid Varieties

Tonie Scroggin

We compute the cohomologies of two strand braid varieties using the two-form present in cluster structures. We confirm these results with proof using Alexander and Poincaré duality…