Mathematical Sciences: Applications of Linkage

点击翻译按钮获取中文摘要

The technique of linkage has been instrumental in attacking a diverse group of problems in commutative algebra. Professors Kustin and Miller will concentrate in this research mainly on the aspects of the theory that involve the interplay of linkage with the structure of finite free resolution of perfect ideals, putting particular emphasis on the multiplicative structures supported on these resolutions. They will also extend this study to the more flexible relation of residual intersection, so that previous techniques can be extended to a wider class of algebras. They are particularly interested in Rees algebras, and algebras defined by sequences and matrices of indeterminates. Applications to determination of rationality of Poincare series and the computation of certain K-groups are expected.