Milnor fiber boundary of a non-isolated surface singularity:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2012
|
| Series: | Lecture notes in mathematics
2037 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | XII, 240 S. graph. Darst. 24 cm |
| ISBN: | 9783642236464 3642236464 9783642236471 |
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| 100 | 1 | |a Némethi, András |e Verfasser |0 (DE-588)1044435046 |4 aut | |
| 245 | 1 | 0 | |a Milnor fiber boundary of a non-isolated surface singularity |c András Némethi ; Ágnes Szilárd |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2012 | |
| 300 | |a XII, 240 S. |b graph. Darst. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Lecture notes in mathematics |v 2037 | |
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| 650 | 0 | 7 | |a Milnor-Faserung |0 (DE-588)4280290-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Hyperflächensingularität |0 (DE-588)4161055-6 |D s |
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Record in the Search Index
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| adam_text |
IMAGE 1
CONTENTS
1 INTRODUCTION 1
1.1 MOTIVATIONS, GOALS AND RESULTS 1
1.2 LIST OF EXAMPLES WITH SPECIAL PROPERTIES 6
PART I PRELIMINARIES
2 THE TOPOLOGY OF A HYPERSURFACE GERM / IN THREE VARIABLES 11 2.1 THE
LINK AND THE MILNOR FIBER F OF HYPERSURFACE SINGULARITIES 11
2.2 GERMS WITH 1 -DIMENSIONAL SINGULAR LOCUS: TRANSVERSAL TYPE. 13 2.3
THE DECOMPOSITION OF THE BOUNDARY OF THE MILNOR FIBER 14
3 THE TOPOLOGY OF A PAIR ( / , #) 17
3.1 BASICS OF ICIS: GOOD REPRESENTATIVES 17
3.2 THE MILNOR OPEN BOOK DECOMPOSITIONS OF DF 20
3.3 THE DECOMPOSITION OF DF REVISITED 20
3.4 RELATION WITH THE NORMALIZATION OF THE ZERO LOCUS OF / 22
4 PLUMBING GRAPHS AND ORIENTED PLUMBED 3-MANIFOLDS 25 4.1 ORIENTED
PLUMBED MANIFOLDS 25
4.2 THE PLUMBING CALCULUS 30
4.3 EXAMPLES: RESOLUTION GRAPHS OF SURFACE SINGULARITIES 35 4.4
EXAMPLES: MULTIPLICITY SYSTEMS AND MILNOR FIBRATIONS 40
5 CYCLIC COVERINGS OF GRAPHS 45
5.1 THE GENERAL THEORY OF CYCLIC COVERINGS 45
5.2 THE UNIVERSAL CYCLIC COVERING OF R(X, F) 47
5.3 THE RESOLUTION GRAPH OF F(X, Y) + Z N = 0 51
6 THE GRAPH T^OFA PAIR ( / , G ): THE DEFINITION 55
6. 1 THE CONSTRUCTION OF THE CURVE E AND ITS DUAL GRAPH 55 6.2 SUMMARY
OF NOTATION FOR /"V AND LOCAL EQUATIONS 57
6.3 ASSUMPTION A 60
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1013868544
DIGITALISIERT DURCH
IMAGE 2
X CONTENTS
7 THE GRAPH TV: PROPERTIES 63
7.1 WHY ONE SHOULD WORK WITH *F? 63
7.2 A PARTITION OF A? AND CUTTING EDGES 65
7.3 THE GRAPH F^ 66
7.4 THE GRAPH R ,| 68
7.5 CUTTING EDGES REVISITED 73
8 EXAMPLES: HOMOGENEOUS SINGULARITIES 79
8.1 THE GENERAL CASE 79
8.2 LINE ARRANGEMENTS 81
9 EXAMPLES: FAMILIES ASSOCIATED WITH PLANE CURVE SINGULARITIES 83 9.1
CYLINDERS OF PLANE CURVE SINGULARITIES 83
9.2 GERMSOFTYPE/ = Z F'(X,Y) 84
9.3 DOUBLE SUSPENSIONS 85
9.4 THE 7/ A ,*,*-FAMILY 95
PART II PLUMBING GRAPHS DERIVED FROM TV
10 THE MAIN ALGORITHM 101
10.1 PREPARATIONS FOR THE MAIN ALGORITHM 101
10.2 THE MAIN ALGORITHM: THE PLUMBING GRAPH OF 3F 102 10.3 PLUMBING
GRAPHS OF 3, F AND B 2 F 107
10.4 FIRST EXAMPLES OFGRAPHS OF 3F, 3, F AND 3 2 F 110
11 PROOF OF THE MAIN ALGORITHM 117
11.1 PRELIMINARY REMARKS 117
11.2 THE GUIDING PRINCIPLE AND THE OUTLINE OF THE PROOF 118 11.3 THE
FIRST STEP: THE REAL VARIETIES Y K 119
11.4 THE STRICT TRANSFORM Y K OF Y K VIA R *_ 121
11.5 LOCAL COMPLEX ALGEBRAIC MOJDELS FOR THE POINTS OF Y K 122
11.6 THE NORMALIZATION^""*' OF Y K 123
11.7 THE "RESOLUTION"^OF Y K 127
11.8 THE PLUMBING GRAPH: THE END OF THE PROOF 128
11.9 THE "EXTENDED" MONODROMY ACTION 129
12 THE COLLAPSING MAIN ALGORITHM 131
12.1 ELIMINATION OF ASSUMPTION B 131
12.2 THE COLLAPSING MAIN ALGORITHM 136
12.3 THE OUTPUT OF THE COLLAPSING MAIN ALGORITHM 1 37
13 VERTICAL/HORIZONTAL MONODROMIES 1 39
13.1 THE MONODROMY OPERATORS 139
13.2 GENERAL FACTS 140
13.3 CHARACTERS: ALGEBRAIC PRELIMINARIES 141
IMAGE 3
CONTENTS XI
13.4 THE DIVISORS D1V4,, DIV? AND DIV'J IN TERMS OF F G 145 13.5
EXAMPLES 148
13.6 VERTICAL MONODROMIES AND THE GRAPH G 149
14 THE ALGEBRAIC MONODROMY OF H\(BF): STARTING POINT 153 14.1 THE PAIR
(3F, 3F \ V G ) 153
14.2 THE FIBRATIONS ARG(G) 154
15 THE RANKS OF H X (DF) AND HI(BF\V G ) VIA PLUMBING 157
15.1 PLUMBING HOMOLOGY AND JORDAN BLOCKS 157
15.2 BOUNDS FORCORANK/4 AND CORANK (A , 3) 159
16 THE CHARACTERISTIC POLYNOMIAL OF 3F VIA P* AND P* 161
16. 1 THE CHARACTERISTIC POLYNOMIAL OF G - /V AND G - DG 161 16.2 THE
CHARACTERISTIC POLYNOMIAL OF 3F 162
17 THE PROOF OF THE CHARACTERISTIC POLYNOMIAL FORMULAE 1 67 17.1
COUNTING JORDAN BLOCKS OF SIZE 2 167
17.2 CHARACTERS 171
18 THE MIXED HODGE STRUCTURE OF I/,(9F) 173
18.1 GENERALITIES: CONJECTURES 1 73
PART III EXAMPLES
19 HOMOGENEOUS SINGULARITIES 179
19.1 THE FIRST SPECIFIC FEATURE: M RER = (M HOR )^_^. 179
19.2 THE SECOND SPECIFIC FEATURE: THE GRAPHS G 2 J 180
19.3 THE THIRD SPECIFIC FEATURE: THE D -COVERING 182
19.4 THE CHARACTERISTIC POLYNOMIAL OF 3F 184
19.5 M' JMR M' JM , MF HOR M* VER AW AND M^, R 186
19.6 WHEN IS DF A RATIONAL/INTEGRAL HOMOLOGY SPHERE? 187 19.7 CASES WITH
D SMALL 188
19.8 RATIONAL UNICUSPIDAL CURVES WITH ONE PUISEUX PAIR 191 19.9 THE
WEIGHT FILTRATION OF THE MIXED HODGE STRUCTURE 194 19.10 LINE
ARRANGEMENTS 1 97
20 CYLINDERS OF PLANE CURVE SINGULARITIES:/ = F'(X,Y) 201
20.1 USING THE MAIN ALGORITHM: THE GRAPH G 201
20.2 COMPARING WITH A DIFFERENT GEOMETRIC CONSTRUCTION 203 20.3 THE
MIXED HODGE STRUCTURE ON //I(3F) 204
21 G E R M S/ OF TYPE ZF'(X,Y) 205
21.1 A GEOMETRIC REPRESENTATION OF F AND 3F 205
22 THE 7".,.,.-FAMILY 209
22.1 THE SERIES TA,,».» 209
22.2 THE SERIES 7^.2.00 209
IMAGE 4
XII CONTENTS
23 GERMS / OF TYPE / (*". *, Z): SUSPENSIONS 211
23.1 / OF TYPE F_(XY,Z) 211
23.2 / OF T Y P E / ( * " /, Z) 212
PART IV WHAT NEXT?
24 PECULIAR STRUCTURES ON DF : TOPICS FOR FUTURE RESEARCH 217 24.1
CONTACT STRUCTURES 217
24.2 TRIPLE PRODUCT: RESONANCE VARIETIES 218
24.3 RELATIONS WITH THE HOMOLOGY OF THE MILNOR FIBER 219 24.4 OPEN
PROBLEMS 220
LIST OF EXAMPLES 223
LIST OF NOTATIONS 225
REFERENCES 231
INDEX 237 |
| any_adam_object | 1 |
| author | Némethi, András Szilárd, Ágnes |
| author_GND | (DE-588)1044435046 |
| author_facet | Némethi, András Szilárd, Ágnes |
| author_role | aut aut |
| author_sort | Némethi, András |
| author_variant | a n an á s ás |
| building | Verbundindex |
| bvnumber | BV039841155 |
| classification_rvk | SI 850 |
| classification_tum | MAT 329f MAT 572f MAT 146f |
| ctrlnum | (OCoLC)744297484 (DE-599)DNB1013868544 |
| dewey-full | 516.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.353 |
| dewey-search | 516.353 |
| dewey-sort | 3516.353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| physical | XII, 240 S. graph. Darst. 24 cm |
| publishDate | 2012 |
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| publisher | Springer |
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| series2 | Lecture notes in mathematics |
| spelling | Némethi, András Verfasser (DE-588)1044435046 aut Milnor fiber boundary of a non-isolated surface singularity András Némethi ; Ágnes Szilárd Berlin [u.a.] Springer 2012 XII, 240 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 2037 Literaturangaben Hyperflächensingularität (DE-588)4161055-6 gnd rswk-swf Milnor-Faserung (DE-588)4280290-8 gnd rswk-swf Hyperflächensingularität (DE-588)4161055-6 s Milnor-Faserung (DE-588)4280290-8 s DE-604 Szilárd, Ágnes Verfasser aut Erscheint auch als Online-Ausgabe Milnor fiber boundary of a non-isolated surface singularity Lecture notes in mathematics 2037 (DE-604)BV000676446 2037 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3859668&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024701056&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Némethi, András Szilárd, Ágnes Milnor fiber boundary of a non-isolated surface singularity Lecture notes in mathematics Hyperflächensingularität (DE-588)4161055-6 gnd Milnor-Faserung (DE-588)4280290-8 gnd |
| subject_GND | (DE-588)4161055-6 (DE-588)4280290-8 |
| title | Milnor fiber boundary of a non-isolated surface singularity |
| title_auth | Milnor fiber boundary of a non-isolated surface singularity |
| title_exact_search | Milnor fiber boundary of a non-isolated surface singularity |
| title_full | Milnor fiber boundary of a non-isolated surface singularity András Némethi ; Ágnes Szilárd |
| title_fullStr | Milnor fiber boundary of a non-isolated surface singularity András Némethi ; Ágnes Szilárd |
| title_full_unstemmed | Milnor fiber boundary of a non-isolated surface singularity András Némethi ; Ágnes Szilárd |
| title_short | Milnor fiber boundary of a non-isolated surface singularity |
| title_sort | milnor fiber boundary of a non isolated surface singularity |
| topic | Hyperflächensingularität (DE-588)4161055-6 gnd Milnor-Faserung (DE-588)4280290-8 gnd |
| topic_facet | Hyperflächensingularität Milnor-Faserung |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3859668&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024701056&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
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