CPL - Chalmers Publication Library
| Utbildning | Forskning | Styrkeområden | Om Chalmers | In English In English Ej inloggad.

An analytic approach to Briancon-Skoda type theorems

Jacob Sznajdman (Institutionen för matematiska vetenskaper)
Göteborg : Chalmers University of Technology, 2012. ISBN: 978-91-7385-688-1.- 105 s.

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.

Nyckelord: Briancon-Skoda theorem, Artin-Rees lemma, Singular varieties, Residue calculus, Milnor number

Denna post skapades 2012-05-07. Senast ändrad 2013-09-25.
CPL Pubid: 157402


Läs direkt!

Lokal fulltext (fritt tillgänglig)

Institutioner (Chalmers)

Institutionen för matematiska vetenskaperInstitutionen för matematiska vetenskaper (GU)



Chalmers infrastruktur


Datum: 2012-05-25
Tid: 13:15
Lokal: Sal Euler, Skeppsgränd 3, Chalmers
Opponent: Prof. Alain Yger, l'Institut de Mathématiques de Bordeaux, France

Ingår i serie

Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie 3369