4 papers · 1 filter
Linear bounds on growth of associated primes
Karen E. Smith, Irena Swanson
We find explicit bounds on the primary components and on the Castelnuovo-Mumford regularity of powers of monomial ideals. We also analyze the primary decompositions of Katzman's ex…
Simplicity of Rings of Differential Operators in Prime Characteristic
Karen E. Smith, Michel Van den Bergh
Let W be a finite dimensional representation of a linearly reductive group G over a field k. Motivated by their work on classical rings of invariants, Levasseur and Stafford asked…
Tight closure commutes with localization in binomial rings
Karen E. Smith
It is proved that tight closure commutes with localization in any domain which has a module finite extension in which tight closure is known to commute with localization. It follow…
Uniform Approximation of Abhyankar Valuation Ideals in Smooth Function Fields
Lawrence Ein, Robert Lazarsfeld, Karen E. Smith
In this paper we use the theory of multiplier ideals to show that the valuation ideals of a rank one Abhyankar valuation centered at a smooth point of a complex algebraic variety a…