The goal of this project is to understand some of the algebraic and geometric properties of points in a multi-projective space. We have focused on understanding when the associated algebraic object is a Cohen-Macaulay ring. In this case, we have discovered a number of properties about the Hilbert functions of points in a multi-projective spaces. A recent (2015) monograph that we wrote summarizes some of the main results in the field.
Impact
Some of our results have been used to study tensors, which are important in areas such as computer vision.
Student Experience
Aspects of this research program can be given to graduate students. For example, a current MSc student is working on developing a Buchberger-Moeller-type algorithm for points in a multi-projective space.
