25 research outputs found
Cohen-Macaulayness of Rees Algebras of Diagonal Ideals
Given two determinantal rings over a field k. We consider the Rees algebra of
the diagonal ideal, the kernel of the multiplication map. The special fiber
ring of the diagonal ideal is the homogeneous coordinate ring of the join
variety. When the Rees algebra and the Symmetric algebra coincide, we show that
the Rees algebra is Cohen-Macaulay.Comment: This work is based on author's Ph. D. thesis from Purdue University
under the direction of Professor Bernd Ulric
Rees Algebras of Diagonal Ideals
There is a natural epimorphism from the symmetric algebra to the Rees algebra
of an ideal. When this epimorphism is an isomorphism, we say that the ideal is
of linear type. Given two determinantal rings over a field, we consider the
diagonal ideal, the kernel of the multiplication map. We prove that the
diagonal ideal is of linear type and recover the defining ideal of the Rees
algebra in some special cases. The special fiber ring of the diagonal ideal is
the homogeneous coordinate ring of the join variety.Comment: This work is based on author's Ph. D. thesis from Purdue University
under the direction of Professor Bernd Ulric
Regularity and multiplicity of toric rings of three-dimensional Ferrers diagrams
We investigate the Castelnuovo--Mumford regularity and the multiplicity of
the toric ring associated to a three-dimensional Ferrers diagram. In
particular, in the rectangular case, we are able to provide direct formulas for
these two important invariants. Then, we compare these invariants for an
accompanied pair of Ferrers diagrams under some mild conditions, and bound the
Castelnuovo--Mumford regularity for more general cases.Comment: 22 pages, 2 figures and comments are welcom