This proposal consists of two parts. The first is concerned with the study of residual intersections and linkage of ideals. The second is the investigation of the various associated blowing-up rings. The underlying theme is to explore connections between the two areas. The investigator studies the Cohen-Macaulayness of symmetric algebras, and the normality and the nature of the defining equations of Rees algebras, by utilizing the methods of residual intersections.
This project in commutative algebra is motivated by closely related problems in algebraic geometry. The process of blowing-up being a fundamental tool in study of the singularities of algebraic varieties, our research of the corresponding algebraic problems will hopefully yield more insight into the geometry.
