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

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

2012-03-02

arxiv.org/abs/1203.0407v1

Journal of Algebra 357 (2012) 279-303

Mathematics

Commutative Algebra

29 pages, 32 figures

Scientific paper

10.1016/j.jalgebra.2012.01.032

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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