Abstract :

In 2008, Boij and Söderberg, stated a couple of conjecture for the extremal rays of Betti cone over the polynomial ring. They also shown that these conjectures imply the Multiplicity conjecture. In 2009, Eisenbud and Schreyer resolve Boij-Söderberg’s conjectures. In this series, we discuss Boij-Söderberg theory for standard graded k-algebras. We note the obstacles in using their techniques in the general situation and identify classes of rings where we can prove some of these results.