Advisor(s)

Venkatramani Lakshmibai

Date of Award

2008

Date Accepted

4-2008

Degree Grantor

Northeastern University

Degree Level

Ph.D.

Degree Name

Doctor of Philosophy

Department or Academic Unit

College of Arts and Sciences. Department of Mathematics.

Keywords

Toric varieties, algebra

Subject Categories

Toric varieties, Algebraic varieties

Disciplines

Mathematics

Abstract

Hibi considered the class of algebras $k[\mathcal{L}]=k[x_{\alpha} \res \alpha \in \mathcal{L}]$ with straightening laws associated to a finite distributive lattice $\mathcal{L}$ in his paper \cite{hibi}. In that paper he proves that these algebras are normal and integral domains. This result along with the work of Sturmfels and Eisenbud \cite{ES} on binomial prime ideals implies that the affine varieties associated to the algebra $k[\mathcal{L}]$ are normal toric varieties. In the present work we will consider the toric variety $X(\mathcal{L})=\mathrm{spec}( k[\mathcal{L}])$, we will give the combinatorial description of the cone $\sigma$ associated to it. The final result will be to give a standard monomial basis for the tangent cone $\widehat{T_{x_\tau}}$ where $x_\tau$ is a singular point associated to a torus orbit $O_\tau$ for the action of the torus $T$, where $\tau$ is a face of the cone $\sigma$

* Due to character limitations, this mathematical expression cannot be accurately rendered here. Please refer to the abstract as included in the full-text PDF for the correct expression.

Document Type

Dissertation

Rights Holder

Himadri Mukherjee


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Mathematics Commons

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