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arXiv · 1203.0407

Ideals generated by 2-minors, collection of cells and stack polyominoes

Ayesha Asloob Qureshi
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Abstract

In this paper we study ideals generated by quite general sets of 2-minors of an $m \times n$-matrix of indeterminates. The sets of 2-minors are defined by collections of cells and include 2-sided ladders. For convex collections of cells it is shown that the attached ideal of 2-minors is a Cohen--Macaulay prime ideal. Primality is also shown for collections of cells whose connected components are row or column convex. Finally the class group of the ring attached to a stack polyomino and its canonical class is computed, and a classification of the Gorenstein stack polyominoes is given.

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Ayesha Asloob Qureshi. 2012-03-02. Ideals generated by 2-minors, collection of cells and stack polyominoes. https://doi.org/10.1016/j.jalgebra.2012.01.032

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