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April, 2008 Rees algebras on smooth schemes: integral closure and higher differential operator
Orlando Villamayor U.
Rev. Mat. Iberoamericana 24(1): 213-242 (April, 2008).


Let $V$ be a smooth scheme over a field $k$, and let $\{I_n, n\geq 0\}$ be a filtration of sheaves of ideals in $\mathcal{O}_V$, such that $I_0=\mathcal{O}_V$, and $I_s\cdot I_t\subset I_{s+t}$. In such case $\bigoplus I_n$ is called a Rees algebra. A Rees algebra is said to be a differential algebra if, for any two integers $N > n$ and any differential operator $D$ of order $n$, $D(I_N)\subset I_{N-n}$. 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. Iberoamericana 24 (1) 213 - 242, April, 2008.


Published: April, 2008
First available in Project Euclid: 16 July 2008

zbMATH: 1151.14013
MathSciNet: MR2435971

Primary: 14E15

Keywords: integral closure , Rees algebras

Rights: Copyright © 2008 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.24 • No. 1 • April, 2008
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