Equidimensional and Unmixed Ideals of Veronese Type

广义Veronese双型理想的纯性

Unmixedness of generalized Veronese bi-type ideals

本文计算了广义Veronese双型理想的代数不变量，刻画了其纯性并描述了相伴素理想。

On certain equidimensional polymatroidal ideals

The class of equidimensional polymatroidal ideals are studied. In particular, we show that an unmixed polymatroidal ideal is connected in codimension one if and only if it is Cohen-Macaulay. Especially a matroidal ideal is connected in codimension one precisely when it is a squarefree Veronese ideal. As a consequence we indicate that for polymatroidal ideals, the Serre's condition $(S_n)$ for some $n\geq 2$ is equivalent to Cohen-Macaulay property. We also give a classification of generalized Cohen-Macaulay polymatroidal ideals.

An improvement upon unmixed decomposition of an algebraic variety

Decomposing an algebraic variety into irreducible or equidimensional components is a fundamental task in classical algebraic geometry and has various applications in modern geometry engineering. Several researchers studied the problem and developed efficient algorithms using $Gr$ö$bner$ basis method. In this paper, we try to modify the computation of unmixed decomposition of an algebraic variety based on improving the computation of $Zero(sat(\mathbb{T}))$, where $\mathbb{T}$ is a triangular set in $\textbf{K[X]}$.