  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.
