IDEALS GENERATED BY 2-MINORS, COLLECTIONS OF CELLS AND STACK POLYOMINOES

By Ayesha Asloob Qureshi. 2012

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Abstract In this paper we study ideals generated by quite general sets of 2-minors of an m × 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.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/1c01c55321410711054ddf3aa2132208fbbc84fa