Seminar

It is known that all ordinary powers of a Stanley-Reisner ideal I_D is Cohen-Macaylay if D is a complete intersection complex. Recently it was found that all symbolic powers of a Stanley-Reisner ideal I_D are Cohen-Macaulay if and only if D is a matroid complex. I will show how one can use tools of integer programming to prove this result.

The next question is when a fixed ordinary or symbolic power of I_D is Cohen-Macaulay. For that I will present a characterization of complexes which are locally matroid or complete intersection complexes. From this it follows that if an ordinary or symbolic power of I_D is Cohen-Macaulay for some power greater than 2, then it will imply that D is a matroid or a complete intersection complex, respectively.