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arXiv · 1806.04446

Quadrics defined by skew-symmetric matrices

Joydip Saha·Indranath Sengupta·Gaurab Tripathi
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Abstract

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 $n$.

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Joydip Saha, Indranath Sengupta, Gaurab Tripathi. 2018-06-12. Quadrics defined by skew-symmetric matrices. https://arxiv.org/abs/1806.04446

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