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Let I be either the ideal of maximal minors or the ideal of 2-minors of a rowgraded or column graded matrix of linear forms L. In two previous papers weshowed that I is a Cartwright-Sturmfels ideal, that is, the multigraded genericinitial ideal gin(I) of I is radical (and essentially independent of the termorder chosen). In this paper we describe generators and prime decomposition ofgin(I) in terms of data related to the linear dependences among the row orcolumns of the submatrices of L. In the case of 2-minors we also give a closedformula for its multigraded Hilbert series.

Multigraded generic initial ideals of determinantal ideals