5 papers
On the quantum parameter in the quantum cohomology of a family of odd symplectic partial flag varieties
Connor Bean, Caleb Shank, Ryan M. Shifler
We will consider a particular family of odd symplectic partial flag varieties denoted by $\mbox{IF}$. In the quantum cohomology ring $\mbox{QH}^*(\mbox{IF})$, we will show that $q_…
Curve neighborhoods and combinatorial property for a family of odd symplectic partial flag manifolds
Connor Bean, Bradley Cruikshank, Ryan M. Shifler
Let be an odd dimensional complex vector space and $\mbox{IF}:=\mbox{IF}(1,2;E)$ be the family of odd symplectic partial flag manifold. In this paper we give a full description…
On the spectral properties of the quantum cohomology of odd quadrics
Ryan M. Shifler, Stephanie Warman
Let $H^\bullet(\mbox{OG})$ be the quantum cohomology (specialized at ) of the dimensional quadric $\mbox{OG}$. We will calculate the characteristic polynomial of the li…
Positivity determines the quantum cohomology of the odd symplectic Grassmannian of lines
Ryan M. Shifler
Let $\mbox{IG}:=\mbox{IG}(2,2n+1)$ denote the odd symplectic Grassmannian of lines which is a horospherical variety of Picard rank 1. The quantum cohomology ring $\mbox{QH}^*(\mbox…
Minimum quantum degrees with Maya diagrams
Ryan M. Shifler
We use Maya diagrams to refine the criterion by Fulton and Woodward for the smallest powers of the quantum parameter that occur in a product of Schubert classes in the (small)…