arXiv subjects
Publications and source records attributed to Joydip Saha.
In this paper we study primality and primary decomposition of certain ideals which are generated by homogeneous degree $2$ polynomials and occur naturally from determinantal conditions. Normality is derived from these results.
In this paper we prove conditions for transversal intersection of monomial ideals and derive a simplicial characterization of this phenomenon.
In this paper we compute Gröbner bases for determinantal ideals of the form $I_{1}(XY)$, where $X$ and $Y$ are both matrices whose entries are indeterminates over a field $K$. We use the Gröbner basis structure to determine Betti numbers for such ideals.
Bresinsky defined a class of monomial curves in $\mathbb{A}^{4}$ with the property that the minimal number of generators or the first Betti number of the defining ideal is unbounded above. We prove that the same behaviour of unboundedness is true for all the Betti numbers and construct an explicit minimal free resolution for this class.
In this paper we propose a model for computing a minimal free resolution for ideals of the form $I_{1}(X_{n}Y_{n})$, where $X_{n}$ is an $n\times n$ skew-symmetric matrix with indeterminate entries $x_{ij}$ and $Y_{n}$ is a generic column matrix with indeterminate entries $y_{j}$. We verify that the model works for $n=3$ and $n=4$ and pose some statements as conjectures. Answering the conjectures in affirmative would enable us to compute a minimal free resolution for general $n$.
In this paper we derive some conditions for transversal intersection of polynomial ideals. We exhibit some examples. Finally, as an application of the results proved, we compute the Betti numbers for ideals of the form $I_{1}(XY) + J$, where $X$ and $Y$ are matrices and $J$ is the ideal generated by the $2\times 2$ minors of the matrix consisting of any two rows of $X$.