Chennai Mathematical Institute


12 noon, Seminar hall
Subadditivity of Maximal shifts in Free Resolutions

Hema Srinivasan
University of Missouri.


S is a polynomial ring over a field, I is a homogeneous ideal of S and R=S/I. F=\sum F_a is a free resolution of R with the grading in the free modules F_a so shifted to make the maps homogeneous of degree zero. Then t_a(F) denotes the maximal shift in F_a. F is said to have subadditivity in maximal shifts if t_{a+b}(F)\leq t_a(F)+T_b(F). The subadditivity problem has been of interest recently. The minimal resolutions of graded algebras will not always have this property. It is as yet not known whether the minimal resolutions of graded algebbras defined by monomial ideals always admit this property. Let p denote the projective dimension of R. In this talk, I will discuss my joint work with Juegen Herzog where we prove t_a \leqt_{a-1}+t_1 for minimal resolutions of graded algebras defined by monomial ideals and t_p \leq t_{p-1}+t_1 for any graded algebra R.