Blow-up algebras, Hilbert functions and local cohomology

My current research focuses on Hilbert functions of admissible filtrations of ideals in Cohen-Macaulay rings. These rings are central objects of study in commutative algebra. Through the knowledge of their Hilbert polynomials we can obtain information about various blow-up algebras such as Rees algebras, associated graded rings and the ring itself. Information about these algebras is often useful in resolution of singularities as demonstrated in the works of Abhyankar, Hironaka, Sally, Zariski and others.

blow up algebras hilbert function