Workshop

Betti numbers and shifts in minimal graded free resolutions

  • Tim Römer (Universität Osnabrück, Germany)
G3 10 (Lecture hall)

Abstract

Let S be a polynomial ring over a field K and let R=S/I be a standard graded K-Algebra where I is a graded ideal of S. The Multiplicity Conjecture of Herzog, Huneke, and Srinivasan which was recently proved using the Boij-Söderberg theory states that the multiplicity of R is bounded above by a function of the maximal shifts in the minimal graded free resolution of R over S as well as bounded below by a function of the minimal shifts if R is Cohen-Macaulay.

We present results to the related problem that the total Betti-numbers of R are also bounded above by a function of the shifts in the minimal graded free resolution of R as well as bounded below by another function of the shifts if R is Cohen-Macaulay.

Max Nitsche

Max-Planck-Institut für Mathematik in den Naturwissenschaften Contact via Mail

Antje Vandenberg

Max-Planck-Institut für Mathematik in den Naturwissenschaften Contact via Mail

Jürgen Jost

Max-Planck-Institut für Mathematik in den Naturwissenschaften

Jürgen Stückrad

Universität Leipzig