Hermitian (a,b)-modules and Saito's "higher residue pairings"

• Autorzy: Piotr P. Karwasz
• Języki publikacji: EN

Abstrakty

EN

Following the work of Daniel Barlet [Pitman Res. Notes Math. Ser. 366 (1997), 19-59] and Ridha Belgrade [J. Algebra 245 (2001), 193-224], the aim of this article is to study the existence of (a,b)-hermitian forms on regular (a,b)-modules. We show that every regular (a,b)-module E with a non-degenerate bilinear form can be written in a unique way as a direct sum of (a,b)-modules $E_i$ that admit either an (a,b)-hermitian or an (a,b)-anti-hermitian form or both; all three cases are possible, and we give explicit examples.
As an application we extend the result of Ridha Belgrade on the existence, for all (a,b)-modules E associated with the Brieskorn module of a holomorphic function with an isolated singularity, of an (a,b)-bilinear non-degenerate form on E. We show that with a small transformation Belgrade's form can be considered (a,b)-hermitian and that the result satisfies the axioms of Kyoji Saito's "higher residue pairings".

Kategorie tematyczne

• 32S40: Monodromy; relations with differential equations and D -modules
• 32S50: Topological aspects: Lefschetz theorems, topological classification, invariants
• 32S25: Surface and hypersurface singularities

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2013
• Tom: 108
• Numer: 3
• Strony: 241-261

Daty

wydano

2013

Twórcy

autor

Piotr P. Karwasz

• Instytut Matematyki, Uniwersytet Gdański, 80-952 Gdańsk, Poland

Identyfikatory

DOI

10.4064/ap108-3-4