Generalizations and applications of border bases:
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| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Passau
2015
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| Subjects: | |
| Online Access: | https://nbn-resolving.org/urn:nbn:de:bvb:739-opus4-3628 Volltext Inhaltsverzeichnis |
| Physical Description: | Xii, 265 Seiten Diagramme |
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Record in the Search Index
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| adam_text | Contents
Abstract v
Zusammenfassung vii
Danksagung ix
1 Introduction 1
2 Border Bases of Finitely Generated Modules 9
2.1 Basic Definitions................................................... 11
2.2 The Border Division Algorithm....................................... 16
2.3 Existence and Uniqueness............................................ 22
2.4 Characterizations................................................... 25
2.4.1 Special Generation............................................ 26
2.4.2 Border Form Modules........................................... 27
2.4.3 Rewrite Rules................................................. 28
2.4.4 Commuting Matrices............................................ 32
2.4.5 Liftings of Border Syzygyies.................................. 41
2.4.6 Buchberger’s Criterion........................................ 48
2.5 Computation......................................................... 50
2.6 Generalized Border Bases............................................ 57
3 Syzygies of Border Bases 67
3.1 Extreme and Non-Extreme Border Terms ...................... 68
3.2 Degree Lowering and Column Clearing................................. 75
3.3 The Reduction Algorithm............................................. 87
3.4 Grobner Bases for the Syzygy Modules of Border Bases................ 97
4 Border Bases and Homogenization 111
4.1 The (Projective) Border Bases Correspondence........................112
4.2 The Multiplicative Structure of a Residue Class Ring Modulo a Proj. Bor-
der Prebasis.............................................................121
4.3 Projective Border Bases and Dualization.............................133
5 Projective Border Bases and Algebraic Geometry 147
5.1 Zero-Dimensional Schemes in Weighted Projective Spaces..............149
5.2 Projective Border Bases and Uniformity Conditions.......................161
5.2.1 The General Case ................................................162
5.2.2 The Reduced Case.................................................173
5.3 Algorithms for Checking Uniformity Conditions...........................177
5.3.1 The General Case ................................................177
5.3.2 The Reduced Case.................................................185
6 The (Projective) Border Basis Scheme 199
6.1 The (Projective) Border Basis Scheme....................................200
6.2 The Multiplicative Structure of the Universal Projective Border Basis Family214
6.3 The Generic Canonical Module of the Universal Projective Border Basis
Family.................................................................227
6.4 Uniformity Conditions...................................................241
7 Conclusion and Outlook 249
Notation 251
Bibliography 259
Publications
265
|
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| spelling | Kriegl, Markus Verfasser aut Generalizations and applications of border bases Markus Kriegl Passau 2015 Xii, 265 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Dissertation Universität Passau 2016 Basis Mathematik (DE-588)4228195-7 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Basis Mathematik (DE-588)4228195-7 s DE-604 Erscheint auch als Online-Ausgabe urn:nbn:de:bvb:739-opus4-3628 https://nbn-resolving.org/urn:nbn:de:bvb:739-opus4-3628 Resolving-System https://opus4.kobv.de/opus4-uni-passau/frontdoor/index/index/docId/362 kostenfrei Volltext Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029010626&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kriegl, Markus Generalizations and applications of border bases Basis Mathematik (DE-588)4228195-7 gnd |
| subject_GND | (DE-588)4228195-7 (DE-588)4113937-9 |
| title | Generalizations and applications of border bases |
| title_auth | Generalizations and applications of border bases |
| title_exact_search | Generalizations and applications of border bases |
| title_full | Generalizations and applications of border bases Markus Kriegl |
| title_fullStr | Generalizations and applications of border bases Markus Kriegl |
| title_full_unstemmed | Generalizations and applications of border bases Markus Kriegl |
| title_short | Generalizations and applications of border bases |
| title_sort | generalizations and applications of border bases |
| topic | Basis Mathematik (DE-588)4228195-7 gnd |
| topic_facet | Basis Mathematik Hochschulschrift |
| url | https://nbn-resolving.org/urn:nbn:de:bvb:739-opus4-3628 https://opus4.kobv.de/opus4-uni-passau/frontdoor/index/index/docId/362 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029010626&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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