IDEALS WITH (d1, . . . , dm)LINEAR QUOTIENTS

In this paper, we introduce the class of ideals with $(d_1,ldots,d_m)$linear quotients generalizing the class of ideals with linear quotients. Under suitable conditions we control the numerical invariants of a minimal free resolution of ideals with $(d_1,ldots,d_m)$linear quotients. In particular we show that their first module of syzygies is a componentwise linear module.