Frontiers in Mathematical Sciences

Linearity of Resolution of Monomial Ideals and the Role of Characteristic of the Base Field

Rashid Zaare-Nahandi


Let $I$ be an ideal generated by monomials of degree $d$ in the polynomial ring over a field $K$. A clutter $C$ can be corresponded to $I$ in a natural way. The aim of this talk is to present some combinatorial conditions on the clutter $C$ which push the resolution of the corresponding ideal to be linear over any field. Some examples of ideals which have a linear resolution over any field except fields of characteristic $p$ for a given prime $p$ will be presented showing how the characteristic of the base field effects on the linearity of the resolution.