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 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”.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap108-3-4,
author = {Piotr P. Karwasz},
title = {Hermitian (a,b)-modules and Saito's "higher residue pairings"},
journal = {Annales Polonici Mathematici},
volume = {107},
year = {2013},
pages = {241-261},
zbl = {1293.32034},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap108-3-4}
}
Piotr P. Karwasz. Hermitian (a,b)-modules and Saito's "higher residue pairings". Annales Polonici Mathematici, Tome 107 (2013) pp. 241-261. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap108-3-4/