Higher Initial Ideals of Homogeneous Ideals

Defines a series of higher initial ideals $\textnormal{in}_s(I)$ for $s\geq0$. This work considers in particular the case where $I$ is the homogeneous ideal of a curve in ${\mathbf P}^3$ and the monomial order is reverse lexicographic. It provides an algebraic approach to studying projective schemes.