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.
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Orlando Villamayor U., Rees algebras on smooth schemes: integral closure and higher differential operator. Rev. Mat. Iberoam. 24 (2008), no. 1, pp. 213–242DOI 10.4171/RMI/534