Rees algebras on smooth schemes: integral closure and higher differential operator

  • Orlando Villamayor U.

    Universidad Autónoma de Madrid, Spain

Abstract

Let be a smooth scheme over a field , and let be a filtration of sheaves of ideals in , such that , and . In such case is called a Rees algebra. A Rees algebra is said to be a differential algebra if, for any two integers and any differential operator of order , . Any Rees algebra extends to a smallest differential algebra. There are two extensions of Rees algebras of interest in singularity theory: one defined by taking integral closures, and another by extending the algebra to a differential algebra. We study here some relations between these two extensions, with particular emphasis on the behavior of higher order differentials over arbitrary fields.

Cite this article

Orlando Villamayor U., Rees algebras on smooth schemes: integral closure and higher differential operator. Rev. Mat. Iberoam. 24 (2008), no. 1, pp. 213–242

DOI 10.4171/RMI/534