Illinois Journal of Mathematics

Fine behavior of symbolic powers of ideals

Melvin Hochster and Craig Huneke

Full-text: Open access


A fundamental property connecting the symbolic powers and the usual powers of ideals in regular rings was discovered by Ein, Lazarsfeld, and Smith in 2001, and later extended by Hochster and Huneke in 2002. In this paper we give further generalizations which give better results in case the quotient of the regular ring by the ideal is F-pure or F-pure type. Our methods also give insight into a conjecture of Eisenbud and Mazur concerning the existence of evolutions. The methods used come from tight closure and reduction to positive characteristic.

Article information

Illinois J. Math., Volume 51, Number 1 (2007), 171-183.

First available in Project Euclid: 20 November 2009

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 13A35: Characteristic p methods (Frobenius endomorphism) and reduction to characteristic p; tight closure [See also 13B22]


Hochster, Melvin; Huneke, Craig. Fine behavior of symbolic powers of ideals. Illinois J. Math. 51 (2007), no. 1, 171--183. doi:10.1215/ijm/1258735331.

Export citation