On the fiber cone of monomial ideals

Abstract

We consider the fiber cone of monomial ideals. It is shown that for monomial ideals $$I\subset K[x,y]$$ of height 2, generated by 3 elements, the fiber cone F(I) of I is a hypersurface ring, and that F(I) has positive depth for interesting classes of height 2 monomial ideals $$I\subset K[x,y]$$ , which are generated by 4 elements. For these classes of ideals, we also show that F(I) is Cohen–Macaulay if and only if the defining ideal J of F(I) is generated by at most 3 elements. In all the cases, a minimal set of generators of J is determined.