In this thesis we examine singularities of surfaces and affine Schubert varieties in the affine Grassmannian $mathcal{G}/mathcal{P}$ of type $A^{(1)}$, by considering the action of a particular torus $widehat{T}$ on $mathcal{G}/mathcal{P}$. Let $Sigma$ be an irreducible $widehat{T}$-stable surface in $mathcal{G}/mathcal{P}$ and let $u$ be an attractive $widehat{T}$-fixed point with $widehat{T}$-stable affine neighborhood $Sigma_u$.
We give a description of the $widehat{T}$-weights of the tangent space $T_u(Sigma)$ of $Sigma$ at $u$, give some conditions under which $Sigma$ is nonsingular at $u$, and provide some explicit criteria for $Sigma_u$ to be normal in terms of the weights of $T_u(Sigma)$. We will also prove a conjecture regarding the singular locus of an affine Schubert variety in $mathcal{G}/mathcal{P}$. / Mathematics
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:AEU.10048/1585 |
| Date | 11 1900 |
| Creators | Cheng, Valerie |
| Contributors | Kuttler, Jochen (Mathematical and Statistical Sciences), Chernousov, Vladimir (Mathematical and Statistical Sciences), Pianzola, Arturo (Mathematical and Statistical Sciences), Penin, Alexander (Physics) |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | en_US |
| Detected Language | English |
| Type | Thesis |
| Format | 233923 bytes, application/pdf |
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