Algorithmic Gauß-Manin Connection

  • This thesis builds a bridge between singularity theory and computer algebra. To an isolated hypersurface singularity one can associate a regular meromorphic connection, the Gauß-Manin connection, containing a lattice, the Brieskorn lattice. The leading terms of the Brieskorn lattice with respect to the weight and V-filtration of the Gauß-Manin connection define the spectral pairs. They correspond to the Hodge numbers of the mixed Hodge structure on the cohomology of the Milnor fibre and belong to the finest known invariants of isolated hypersurface singularities. The differential structure of the Brieskorn lattice can be described by two complex endomorphisms A0 and A1 containing even more information than the spectral pairs. In this thesis, an algorithmic approach to the Brieskorn lattice in the Gauß-Manin connection is presented. It leads to algorithms to compute the complex monodromy, the spectral pairs, and the differential structure of the Brieskorn lattice. These algorithms are implemented in the computer algebra system Singular.
  • Algorithmic Gauß-Manin Connection

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Metadaten
Author:Mathias Schulze
URN (permanent link):urn:nbn:de:bsz:386-kluedo-13943
Advisor:H. von Weizsäcker
Document Type:Doctoral Thesis
Language of publication:English
Year of Completion:2002
Year of Publication:2002
Publishing Institute:Technische Universität Kaiserslautern
Granting Institute:Technische Universität Kaiserslautern
Acceptance Date of the Thesis:2002/07/17
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:510 Mathematik

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