Semistable extension of families of curves:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
2014
|
| Schlagworte: | |
| Online-Zugang: | kostenfrei https://nbn-resolving.org/urn:nbn:de:bvb:355-epub-307306 Inhaltsverzeichnis |
| Beschreibung: | 74 Bl. |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804152505049808896 |
|---|---|
| adam_text | CONTENTS
1 INTRODUCTION
2 NORMALITY AND GLUING ALONG SECTIONS 2
2.1 PRODUCT 2
2.1.1 PRODUCT ALONG ARBITRARY BASE SCHEME 2
2.1.2 FIBRES OF MORPHISMS 3
2.2 BASE CHANGE 4
2.2.1 EXTENDING VARIETIES TO ALGEBRAICALLY CLOSED FIELD 5
2.2.2 RATIONAL POINTS OF GEOMETRICALLY REDUCED VARIETIES 7
2.3 SOME GLOBAL PROPERTIES 8
2.3.1 SEPARATEDNESS 8
2.3.2 PROPEMESS 9
2.3.3 EXTENDING OF RATIONAL POINTS 9
2.3.4 COMPACTIFICATIONS OF SCHEMES AND CHOW S LEMMA 10
2.4 NORMALITY 11
2.4.1 EXTENDING MORPHISM TO POINTS OF CODIMENSION 1 12
2.4.2 A CRITERION FOR NORMALITY 12
2.4.3 INTEGRAL CLOSURE OF DEDEKIND RINGS 14
2.4.4 THE RELATION BETWEEN REGULARITY AND NORMALITY 15
2.5 SMOOTHNESS 16
2.5.1 A CRITERION FOR FLATNESS 16
2.5.2 DIMENSION OF FIBRES 17
2.5.3 ETALE MORPHISMS 18
2.5.4 RELATION BETWEEN REGULARITY AND SMOOTHNESS 19
2.6 DIVISORS 20
2.6.1 CARTIER DIVISORS 20
2.6.2 WEIL DIVISORS 21
2.6.3 RELATION BETWEEN CARTIER DIVISORS AND WEIL DIVISORS 22
2.6.4 MEETING TRANSVERSALLY 23
HTTP://D-NB.INFO/1058696270
2.6.5 INTERSECTION WITH HORIZONTAL DIVISORS 24
2.6.6 EXCEPTIONAL DIVISORS AND VAN
DER WAERDEN S PURITY THEOREM . . 24
2.7 ABELIAN VARIETIES 25
2.7.1 GROUP SCHEMES 25
2.7.2 JACOBIAN OF CURVES 28
2.7.3 FINITE GROUP SCHEMES AND TORSIONS 30
2.7.4 TATE MODULES 32
2.7.5 ORDINARY ABELIAN VARIETY 32
3 FIBERED SURFACES AND REGULAR MODELS 34
3.1 BASIC PROPERTIES OF FIBERED SURFACES 34
3.1.1 LOCAL PROPERTIES OF FIBERED SURFACES 35
3.1.2 RELATION BETWEEN GENERIC FIBRE AND CLOSED FIBRES 36
3.1.3 SMOOTH LOCUS OF FIBERED SURFACES 37
3.2 DESINGULARISATION 37
3.2.1 HIRONAKA S THEOREM 37
3.2.2 ALTERATION AND A THEOREM BY DE JONG 38
3.2.3 EXISTENCE OF DESINGULARISATION IN SOME CERTAIN CASES 38
3.2.4 EMBEDDED RESOLUTION OF SINGULARITIES (OF CURVES) 39
3.3 REGULAR MODELS 40
3.3.1 REDUCTION 41
4 SEMI-STABLE CURVES 43
4.1 ORDINARY DOUBLE POINTS 43
4.2 SEMI-STABLE CURVES 44
4.2.1 BASIC FACTS ABOUT SEMI-STABLE CURVES 45
5 SEMI-STABLE REDUCTION THEOREMS AND SOME OF THE MAIN RESULTS 47
5.1 SOME GENERALISATIONS OF THE STABLE REDUCTION THEOREM 47
5.2 ALGEBRAIC STACKS AND PROPERNESS OF
M
G
48
5.3 MAIN RESULTS 53
6 A MONODROMY CRITERION FOR EXTENDING FAMILIES OF CURVES 63
6.1 INTRODUCTION AND PREREQUISITE NOTIONS 63
6.2 COUNTEREXAMPLE 66
6.3 MAIN THEOREM 67
6.4 EXTENDING FAMILIES OF CURVES 69
|
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| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| indexdate | 2024-07-10T01:11:46Z |
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| language | English |
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| physical | 74 Bl. |
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| spelling | Dashtpeyma, Mohammad Verfasser aut Semistable extension of families of curves vorgelegt von Mohammad Dashtpeyma 2014 74 Bl. txt rdacontent n rdamedia nc rdacarrier Regensburg, Univ., Diss., 2014 (DE-588)4113937-9 Hochschulschrift gnd-content Erscheint auch als Online-Ausgabe urn:nbn:de:bvb:355-epub-307306 http://epub.uni-regensburg.de/30730/ Verlag kostenfrei Volltext https://nbn-resolving.org/urn:nbn:de:bvb:355-epub-307306 Resolving-System DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027505418&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dashtpeyma, Mohammad Semistable extension of families of curves |
| subject_GND | (DE-588)4113937-9 |
| title | Semistable extension of families of curves |
| title_auth | Semistable extension of families of curves |
| title_exact_search | Semistable extension of families of curves |
| title_full | Semistable extension of families of curves vorgelegt von Mohammad Dashtpeyma |
| title_fullStr | Semistable extension of families of curves vorgelegt von Mohammad Dashtpeyma |
| title_full_unstemmed | Semistable extension of families of curves vorgelegt von Mohammad Dashtpeyma |
| title_short | Semistable extension of families of curves |
| title_sort | semistable extension of families of curves |
| topic_facet | Hochschulschrift |
| url | http://epub.uni-regensburg.de/30730/ https://nbn-resolving.org/urn:nbn:de:bvb:355-epub-307306 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027505418&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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