Standard bases for coordinate rings of cotangent varieties
We extend the results of the Standard Monomial Theory to the cotangent variety of the Grassmannian, $TGrass(k,n)$. We exhibit a standard basis in terms of triples of tableaux. We are also able to show that $TGrass(k,n)$ is arithmetically Cohen-Macaulay and normal in all characteristics. Results on C...
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| Online Access: | http://hdl.handle.net/2047/d20000272 |
| Summary: | We extend the results of the Standard Monomial Theory to the cotangent variety of the Grassmannian, $TGrass(k,n)$. We exhibit a standard basis in terms of triples of tableaux. We are also able to show that $TGrass(k,n)$ is arithmetically Cohen-Macaulay and normal in all characteristics. Results on Cohen-Macaulayness and normality are shown for other algebraic groups and cominuscule parabolic subgroups, but only in characteristic zero. |
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