The Lefschetz properties:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2013
|
| Series: | Lecture notes in mathematics
2080 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XIX, 250 S. graph. Darst. 235 mm x 155 mm |
| ISBN: | 3642382053 9783642382055 |
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MARC
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| 245 | 1 | 0 | |a The Lefschetz properties |c Tadahito Harima ... |
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Record in the Search Index
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| adam_text |
CONTENTS
1 POSET THEORY 1
1.1 POSET AND DILWORTH NUMBER 1
1.2 RANKED POSETS AND THE SPERNER PROPERTY 7
1.3 THE DILWORTH LATTICE 10
1.4 EXAMPLES OF POSETS WITH THE SPERNER PROPERTY 14
1.4.1 BOOLEAN LATTICE 15
1.4.2 THE DIVISOR LATTICE AND FINITE CHAIN PRODUCT 19
1.4.3 PARTITIONS OF INTEGERS 22
1.4.4 THE VECTOR SPACE LATTICES 29
2 BASICS ON THE THEORY OF LOCAL RINGS 39
2.1 MINIMAL GENERATING SET OF AN IDEAL AND NUMBER OF GENERATORS 39
2.1.1 GRADED RINGS 43
2.1.2 ARTINIAN LOCAL RINGS 44
2.1.3 THE TYPE OF AN M-PRIMARY IDEAL 46
2.2 COMPLETE LOCAL RINGS AND MATLIS DUALITY 48
2.2.1 APPLICATION OF THE STRUCTURE THEOREM 49
2.2.2 INJECTIVE MODULES OVER COMMUTATIVE NOETHERIAN RINGS 51
2.2.3 GORENSTEIN LOCAL RINGS AND COHEN-MACAULAY RINGS 52
2.3 IDEALS OF FINITE COLENGTH AND ARTINIAN LOCAL RINGS 55
2.3.1 DILWORTH NUMBER AND REES NUMBER OF ARTINIAN
LOCAL RINGS 56
2.3.2 MONOMIAL ARTINIAN RINGS AND THE DILWORTH NUMBER 60
2.3.3 POSET OF STANDARD MONOMIALS AS A BASIS
FOR MONOMIAL ARTINIAN RINGS 61
2.3.4 THE SPERNER PROPERTY OF ARTINIAN LOCAL RINGS 62
2.3.5 THE DILWORTH LATTICE OF IDEALS 65
2.3.6 M-FULL IDEALS 68
2.4 ARTINIAN GORENSTEIN RINGS 70
2.4.1 THE INVERSE SYSTEM OF MACAULAY 72
2.4.2 A VARIATION OF THE INVERSE SYSTEM 73
XVII
HTTP://D-NB.INFO/1033487627
XVIII CONTENTS
2.4.3 THE RING OF INVARIANTS OF BINARY OCTAVICS
AND HEIGHT THREE GORENSTEIN IDEALS 79
2.4.4 THE PRINCIPLE OF IDEALIZATION AND LEVEL ALGEBRAS 81
2.5 COMPLETE INTERSECTIONS 84
2.6 HILBERT FUNCTIONS 90
3 LEFSCHETZ PROPERTIES 97
3.1 WEAK LEFSCHETZ PROPERTY 97
3.2 STRONG LEFSCHETZ PROPERTY 99
3.3 THE LIE ALGEBRA 5(2 AND ITS REPRESENTATIONS 105
3.3.1 THE LIE ALGEBRA 5(2 105
3.3.2 IRREDUCIBLE MODULES OF 5(2 108
3.3.3 COMPLETE REDUCIBILITY 109
3.3.4 THE CLEBSCH-GORDAN THEOREM 110
3.3.5 THE SLP AND ST
2
112
3.3.6 THE SLP WITH SYMMETRIC HILBERT FUNCTION AND 5(2 117
3.4 THE WLP AND SLP IN LOW CODIMENSIONS 121
3.4.1 THE WLP AND SLP IN CODIMENSION TWO 121
3.4.2 THE WLP IN CODIMENSION THREE 122
3.4.3 THE WLP OF ALMOST COMPLETE INTERSECTION
IN CODIMENSION THREE 125
3.5 JORDAN DECOMPOSITIONS AND TENSOR PRODUCTS 126
3.6 SLP FOR ARTINIAN GORENSTEIN ALGEBRAS AND HESSIANS 135
4 COMPLETE INTERSECTIONS WITH THE SLP 141
4.1 CENTRAL SIMPLE MODULES 141
4.2 FINITE FREE EXTENSIONS OF A GRADED/C-ALGEBRA 144
4.3 POWER SUMS OF CONSECUTIVE DEGREES 149
4.4 MORE APPLICATIONS OF FINITE FREE EXTENSIONS 152
5 A GENERALIZATION OF LEFSCHETZ ELEMENTS 157
5.1 WEAK REES ELEMENTS 157
5.2 STRONG REES ELEMENTS 162
5.3 SOME PROPERTIES OF STRONG REES ELEMENTS 165
5.4 GORENSTEIN ALGEBRAS WITH THE WLP BUT NOT HAVING THE SLP 168
6 K
-LEFSCHETZ PROPERTIES 171
6.1 FC-SLP AND /C-WLP 171
6.1.1 DEFINITIONS 171
6.1.2 BASIC PROPERTIES 172
6.1.3 ALMOST REVLEX IDEALS 176
6.2 CLASSIFICATION OF HILBERT FUNCTIONS 178
6.2.1 HILBERT FUNCTIONS OF A:-SLP AND K-WLP 178
6.2.2 HILBERT FUNCTIONS OF ARTINIAN COMPLETE INTERSECTIONS 181
6.3 GENERIC INITIAL IDEALS 183
6.4 GRADED BETTI NUMBERS 185
CONTENTS XIX
7 COHOMOLOGY RINGS AND THE STRONG LEFSCHETZ PROPERTY 189
7.1 HARD LEFSCHETZ THEOREM 189
7.2 NUMERICAL CRITERION FOR AMPLENESS 191
7.3 COHOMOLOGY RINGS 191
7.3.1 PROJECTIVE SPACE BUNDLE 192
7.3.2 HOMOGENEOUS SPACES 192
7.3.3 TORIC VARIETY 193
7.3.4 O-SEQUENCES 198
8 INVARIANT THEORY AND LEFSCHETZ PROPERTIES 201
8.1 REFLECTION GROUPS 201
8.2 COINVARIANT ALGEBRAS 204
8.2.1 BGGH POLYNOMIAL 205
8.2.2 COINVARIANT ALGEBRA 205
8.2.3 COMPLEX REFLECTION GROUPS 208
9 THE STRONG LEFSCHETZ PROPERTY AND THE SCHUR-WEYL DUALITY 211
9.1 THE SCHUR-WEYL DUALITY 211
9.2 AN EXAMPLE 214
9.3 SPECHT POLYNOMIALS 216
9.4 IRREDUCIBLE DECOMPOSITION OF /\Q 219
9.4.1 EXAMPLES 220
9.4.2 GENERAL CASE 221
9.4.3 THE ^-ANALOG OF THE WEYL DIMENSION FORMULA 223
9.4.4 THE ^-ANALOG OF THE HOOK LENGTH FORMULA 229
9.5 THE HOMOMORPHISM Z : GL(K)GL(K") 232
A THE WLP OF TERNARY MONOMIAL COMPLETE INTERSECTIONS
IN POSITIVE CHARACTERISTIC 235
REFERENCES 239
INDEX 247 |
| any_adam_object | 1 |
| building | Verbundindex |
| bvnumber | BV041271623 |
| classification_rvk | SI 850 |
| classification_tum | MAT 140f MAT 135f |
| ctrlnum | (OCoLC)864650286 (DE-599)DNB1033487627 |
| dewey-full | 512.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.5 |
| dewey-search | 512.5 |
| dewey-sort | 3512.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| physical | XIX, 250 S. graph. Darst. 235 mm x 155 mm |
| publishDate | 2013 |
| publishDateSearch | 2013 |
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| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | The Lefschetz properties Tadahito Harima ... Berlin [u.a.] Springer 2013 XIX, 250 S. graph. Darst. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 2080 Artinsche Algebra (DE-588)4143137-6 gnd rswk-swf Lefschetz-Fixpunktsatz (DE-588)4501113-8 gnd rswk-swf Artinsche Algebra (DE-588)4143137-6 s Lefschetz-Fixpunktsatz (DE-588)4501113-8 s DE-604 Harima, Tadahito Sonstige oth Erscheint auch als Online-Ausgabe 978-3-642-38206-2 Lecture notes in mathematics 2080 (DE-604)BV000676446 2080 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4297169&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=026245225&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | The Lefschetz properties Lecture notes in mathematics Artinsche Algebra (DE-588)4143137-6 gnd Lefschetz-Fixpunktsatz (DE-588)4501113-8 gnd |
| subject_GND | (DE-588)4143137-6 (DE-588)4501113-8 |
| title | The Lefschetz properties |
| title_auth | The Lefschetz properties |
| title_exact_search | The Lefschetz properties |
| title_full | The Lefschetz properties Tadahito Harima ... |
| title_fullStr | The Lefschetz properties Tadahito Harima ... |
| title_full_unstemmed | The Lefschetz properties Tadahito Harima ... |
| title_short | The Lefschetz properties |
| title_sort | the lefschetz properties |
| topic | Artinsche Algebra (DE-588)4143137-6 gnd Lefschetz-Fixpunktsatz (DE-588)4501113-8 gnd |
| topic_facet | Artinsche Algebra Lefschetz-Fixpunktsatz |
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