Koszul cohomology and algebraic geometry:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2010]
|
| Schriftenreihe: | University lecture series
volume 52 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | viii, 125 Seiten |
| ISBN: | 9780821849644 |
Internformat
MARC
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| 008 | 091210s2010 |||| 00||| eng d | ||
| 020 | |a 9780821849644 |c pbk. |9 978-0-8218-4964-4 | ||
| 035 | |a (OCoLC)460710701 | ||
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| 100 | 1 | |a Aprodu, Marian |e Verfasser |0 (DE-588)1101701064 |4 aut | |
| 245 | 1 | 0 | |a Koszul cohomology and algebraic geometry |c Marian Aprodu, Jan Nagel |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2010] | |
| 264 | 4 | |c © 2010 | |
| 300 | |a viii, 125 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a University lecture series |v volume 52 | |
| 650 | 4 | |a Geometry, Algebraic | |
| 650 | 4 | |a Homology theory | |
| 650 | 4 | |a Koszul algebras | |
| 650 | 0 | 7 | |a Homologietheorie |0 (DE-588)4141714-8 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Algebraische Geometrie |0 (DE-588)4001161-6 |D s |
| 689 | 0 | 2 | |a Homologietheorie |0 (DE-588)4141714-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Nagel, Jan |d 1983- |e Verfasser |0 (DE-588)140849505 |4 aut | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-018733873 | ||
Datensatz im Suchindex
| _version_ | 1804140853244985344 |
|---|---|
| adam_text | Contents
Preface
Chapter
1.
Basic definitions
1
1.1.
The
Koszul
complex
1
1.2.
Definitions in the algebraic context
2
1.3.
Minimal resolutions
4
1.4.
Definitions in the geometric context
5
1.5.
Punctorial properties
7
1.6.
Notes and comments
11
Chapter
2.
Basic results
13
2.1.
Kernel bundles
13
2.2.
Projections and linear sections
15
2.3.
Duality
20
2.4.
Koszul
cohomology versus usual cohomology
22
2.5.
Sheaf regularity
24
2.6.
Vanishing theorems
25
2.7.
Notes and comments
27
Chapter
3.
Syzygy schemes
29
3.1.
Basic definitions
29
3.2.
Koszul
classes of low rank
37
3.3.
The KPti theorem
39
3.4.
Rank-2 bundles and
Koszul
classes
43
3.5.
The curve case
46
3.6.
Notes and comments
50
Chapter
4.
The conjectures of Green and Green-Lazarsfeld
53
4.1.
Brill-Noether theory
53
4.2.
Numerical invariants of curves
55
4.3.
Statement of the conjectures
57
4.4.
Generalizations of the Green conjecture
60
4.5.
Notes and comments
63
Chapter
5.
Koszul
cohomology and the Hubert scheme
65
5.1.
Voisin s description
65
5.2.
Examples
68
5.3.
Vanishing via base change
72
Chapter
6.
Koszul
cohomology of
а КЗ
surface
75
6.1.
The
Serre
construction, and vector bundles on
КЗ
surfaces
75
vi
CONTENTS
6.2.
Brill-Noether
theory of curves on
КЗ
surfaces
76
6.3.
Voisin s proof of Green s generic conjecture: even genus
79
6.4.
The odd-genus case (outline)
88
6.5.
Notes and comments
90
Chapter
7.
Specific versions of the syzygy conjectures
91
7.1.
Nodal curves on
КЗ
surfaces
91
7.2.
The specific Green conjecture
92
7.3.
Stable curves with extra-syzygies
95
7.4.
Curves with small Brill-Noether loci
97
7.5.
Further evidence for the Green-Lazarsfeld conjecture
100
7.6.
Exceptional curves
103
7.7.
Notes and comments
103
Chapter
8.
Applications
105
8.1.
Koszul cohomology
and Hodge theory
105
8.2.
Koszul
divisors of small slope on the moduli space. Ill
8.3.
Slopes of fibered surfaces
115
8.4.
Notes and comments
116
Bibliography
119
Index
125
|
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| author | Aprodu, Marian Nagel, Jan 1983- |
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| classification_rvk | SK 240 |
| ctrlnum | (OCoLC)460710701 (DE-599)BVBBV035876196 |
| dewey-full | 512/.46 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.46 |
| dewey-search | 512/.46 |
| dewey-sort | 3512 246 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV035876196 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:06:34Z |
| institution | BVB |
| isbn | 9780821849644 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018733873 |
| oclc_num | 460710701 |
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| physical | viii, 125 Seiten |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | University lecture series |
| series2 | University lecture series |
| spelling | Aprodu, Marian Verfasser (DE-588)1101701064 aut Koszul cohomology and algebraic geometry Marian Aprodu, Jan Nagel Providence, Rhode Island American Mathematical Society [2010] © 2010 viii, 125 Seiten txt rdacontent n rdamedia nc rdacarrier University lecture series volume 52 Geometry, Algebraic Homology theory Koszul algebras Homologietheorie (DE-588)4141714-8 gnd rswk-swf Koszul-Algebra (DE-588)4654529-3 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Koszul-Algebra (DE-588)4654529-3 s Algebraische Geometrie (DE-588)4001161-6 s Homologietheorie (DE-588)4141714-8 s DE-604 Nagel, Jan 1983- Verfasser (DE-588)140849505 aut Erscheint auch als Online-Ausgabe 978-1-4704-1647-8 University lecture series volume 52 (DE-604)BV004153846 52 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018733873&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Aprodu, Marian Nagel, Jan 1983- Koszul cohomology and algebraic geometry University lecture series Geometry, Algebraic Homology theory Koszul algebras Homologietheorie (DE-588)4141714-8 gnd Koszul-Algebra (DE-588)4654529-3 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| subject_GND | (DE-588)4141714-8 (DE-588)4654529-3 (DE-588)4001161-6 |
| title | Koszul cohomology and algebraic geometry |
| title_auth | Koszul cohomology and algebraic geometry |
| title_exact_search | Koszul cohomology and algebraic geometry |
| title_full | Koszul cohomology and algebraic geometry Marian Aprodu, Jan Nagel |
| title_fullStr | Koszul cohomology and algebraic geometry Marian Aprodu, Jan Nagel |
| title_full_unstemmed | Koszul cohomology and algebraic geometry Marian Aprodu, Jan Nagel |
| title_short | Koszul cohomology and algebraic geometry |
| title_sort | koszul cohomology and algebraic geometry |
| topic | Geometry, Algebraic Homology theory Koszul algebras Homologietheorie (DE-588)4141714-8 gnd Koszul-Algebra (DE-588)4654529-3 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| topic_facet | Geometry, Algebraic Homology theory Koszul algebras Homologietheorie Koszul-Algebra Algebraische Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018733873&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004153846 |
| work_keys_str_mv | AT aprodumarian koszulcohomologyandalgebraicgeometry AT nageljan koszulcohomologyandalgebraicgeometry |