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

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Karwasz P.

Annales Polonici Mathematici

2013

tom 108

nr 3

241-261

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".

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1 Annales Polonici Mathematici

1 Karwasz P.

1 2013

Wyniki wyszukiwania

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