Rees algebras of diagonal ideals

Kuei-Nuan Lin, Purdue University

Abstract

Given two varieties, we can construct the embedded join variety. The homogeneous coordinate ring of this variety is the special fiber ring of the diagonal ideal of the original varieties. The varieties we consider here are determinantal varieties. The special fiber rings are understood in this case. However, we do more: we study the Rees algebras of the diagonal ideals. We use Groebner bases as a tool to find the defining equations of the Rees algebras. We prove the Cohen-Macaulayness of these algebras. To do so we use the initial ideals of the ideals defining the Rees algebras and pass to the Alexander duals of these initial ideals.

Degree

Ph.D.

Advisors

Ulrich, Purdue University.

Subject Area

Mathematics

COinS