An analytic approach to Briancon-Skoda type theorems
Doctoral thesis, 2012

The Briancon-Skoda theorem can be seen as an effective version of the Hilbert Nullstellensatz and gives a connection between size conditions on holomorphic functions and ideal membership. The size conditions are captured algebraically by the notion of integral closure of ideals. Many techniques have been applied to prove the Briancon-Skoda theorem and variations of it. The first proof by Briancon and Skoda used L^2-theory. Later, Lipman and Tessier observed that residue calculus could be used to obtain an alternative proof, and inspired by this approach they generalized the theorem to an algebraic setting. Berenstein-Yger et al. developed further this residue method by introducing a division formula by Berndtsson into the picture. The theory of tight closure, introduced by Hochster and Huneke, was motivated by, and has been used to prove, the Briancon-Skoda theorem. This thesis explores how one can use analytic methods, including residue theory, to obtain Briancon-Skoda type theorems on singular varieties.

Milnor number

Briancon-Skoda theorem

Residue calculus

Singular varieties

Artin-Rees lemma

Sal Euler, Skeppsgränd 3, Chalmers
Opponent: Prof. Alain Yger, l'Institut de Mathématiques de Bordeaux, France

Author

Jacob Sznajdman

University of Gothenburg

Chalmers, Mathematical Sciences

Subject Categories

Mathematics

ISBN

978-91-7385-688-1

Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 3369

Sal Euler, Skeppsgränd 3, Chalmers

Opponent: Prof. Alain Yger, l'Institut de Mathématiques de Bordeaux, France

More information

Created

10/8/2017