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

Piotr P. Karwasz. "Hermitian (a,b)-modules and Saito's "higher residue pairings"." Annales Polonici Mathematici 108.3 (2013): 241-261. <http://eudml.org/doc/280293>.

@article{PiotrP2013,
abstract = {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”.},
author = {Piotr P. Karwasz},
journal = {Annales Polonici Mathematici},
keywords = {Brieskorn lattice; -module; duality of -modules; higher residue pairings},
language = {eng},
number = {3},
pages = {241-261},
title = {Hermitian (a,b)-modules and Saito's "higher residue pairings"},
url = {http://eudml.org/doc/280293},
volume = {108},
year = {2013},
}

TY - JOUR
AU - Piotr P. Karwasz
TI - Hermitian (a,b)-modules and Saito's "higher residue pairings"
JO - Annales Polonici Mathematici
PY - 2013
VL - 108
IS - 3
SP - 241
EP - 261
AB - 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”.
LA - eng
KW - Brieskorn lattice; -module; duality of -modules; higher residue pairings
UR - http://eudml.org/doc/280293
ER -