Algebra Seminar: Hugh Geller, Clemson Unversity, USA
Speaker: Hugh Geller, Clemson University, USA
Title: Explicit Minimal Free Resolutions of Fiber Products
Abstract: In 2006, Visscher gave an explicit construction for the minimal free resolution of the fiber product k[x] ×k k[y] ∼= k[x, y]/hxyi over k[x, y]. In this talk, we give an alternate description of Visschers resolution which we then use to resolve quotient rings (with certain constraints) of the form R/hI 0 , IJ, J0 i over R. We then show that this construction can be used to obtain minimal resolutions of fiber products and provides us with explicit formulas for the Betti numbers, Betti tables, and Poincar`e Series.