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
Author: | Mathias Schulze |
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URN: | urn:nbn:de:bsz:386-kluedo-13943 |
Advisor: | Gert-Martin Greuel |
Document Type: | Doctoral Thesis |
Language of publication: | English |
Year of Completion: | 2002 |
Year of first Publication: | 2002 |
Publishing Institution: | Technische Universität Kaiserslautern |
Granting Institution: | Technische Universität Kaiserslautern |
Acceptance Date of the Thesis: | 2002/07/17 |
Date of the Publication (Server): | 2002/07/26 |
Faculties / Organisational entities: | Kaiserslautern - Fachbereich Mathematik |
DDC-Cassification: | 5 Naturwissenschaften und Mathematik / 510 Mathematik |
Licence (German): | Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011 |