The generic ring and structure theorems for free resolutions of length 3

Abstract:  A classical problem in commutative algebra is the classification of the ideals of a ring according to their minimal free resolution.  After briefly recalling the most important known results, we describe how the generic ring associated to a given format of free resolution of length 3 offers new tools to attack this problem.  For ideals with sufficiently small Betti numbers, we discuss the existence of a second complex, canonically associated to the minimal free resolution, mentioning some possible applications in algebra and geometry.  (Joint work with Jerzy Weyman).