Holomorphic vector bundles on
Séminaire Bourbaki (1978-1979)
- Volume: 21, page 80-102
- ISSN: 0303-1179
Access Full Article
topHow to cite
topSchneider, Michael. "Holomorphic vector bundles on $\mathbb {P}_n$." Séminaire Bourbaki 21 (1978-1979): 80-102. <http://eudml.org/doc/109947>.
@article{Schneider1978-1979,
author = {Schneider, Michael},
journal = {Séminaire Bourbaki},
keywords = {Bibliography; classification of holomorphic vector bundles},
language = {eng},
pages = {80-102},
publisher = {Springer-Verlag},
title = {Holomorphic vector bundles on $\mathbb \{P\}_n$},
url = {http://eudml.org/doc/109947},
volume = {21},
year = {1978-1979},
}
TY - JOUR
AU - Schneider, Michael
TI - Holomorphic vector bundles on $\mathbb {P}_n$
JO - Séminaire Bourbaki
PY - 1978-1979
PB - Springer-Verlag
VL - 21
SP - 80
EP - 102
LA - eng
KW - Bibliography; classification of holomorphic vector bundles
UR - http://eudml.org/doc/109947
ER -
References
top- [1] M.F. Atiyah, N.J. Hitchin, V.G. Drinfeld, Ju. Manin - Construction of instantons, Physics Letters, 65A (1978), 185-187. Zbl0424.14004MR598562
- [2] M.F. Atiyah, E. Rees - Vector bundles on projective 3-space, Inventiones math., 35 (1976), 131-153. Zbl0332.32020MR419852
- [3] W. Barth - Submanifolds of low codimension in projective space, Proc. I.C.M. Vancouver (1975), 409-413. Zbl0349.14024MR422294
- [4] W. Barth - Some properties of stable rank -2 vector bundles on Pn , Math. Ann., 226 (1977), 125-150. Zbl0332.32021MR429896
- [5] W. Berth - Moduli of vector bundles on the projective plane, Inventiones math.42 ( 1977), 63-91. Zbl0386.14005MR460330
- [6] W. Barth - Stable vector bundles on P3 , some experimental data, Preprint 1978.
- [7] W. Barth, G. Elencwajg - Concernant la cohomologie des fibrés algébriques stables sur Pn (C) . In Variétés Analytiques Compactes, Nice 1977, Lecture Notes in Math., 683 (1978), 1-24. Zbl0381.55005MR517517
- [8] W. Barth, K. Hulek - Monads and moduli of vector bundles, Manuscripta math.25(1978), 323-347. Zbl0395.14007MR509589
- [9] W. Barth, A. van de Ven - A decomposability criterion for algebraic 2-bundles on projective spaces, Inventiones Math., 25 (1974), 91-106. Zbl0295.14006MR379515
- [10] W. Barth, A. van de Van - On the geometry in codimension 2 of Grassmann manifolds, In classification of algebraic varieties and compact complex manifolds, Lecture Notes in Math., 412 (1974), 1-35. Zbl0299.14024MR354661
- [11] A. Beilinson - Coherent sheaves on PN and problems of linear algebra, J. of functional analysis and its applications, 12 (1978), 68-69. Zbl0402.14006MR509388
- [12] V.G. Drinfeld, Ju. Manin - On locally free sheaves over P3 connected with Yang-Mills fields, Uspechi, 33 (1978), 165-166. Zbl0399.14008MR498569
- [13] V.G. Drinfeld, Ju. Manin - J. Functional Analysis and its applications, 12(1978), 78-79. Zbl0402.53040
- [14] G. Elencwajg - Les fibrés uniformes de rang 3 sur P2(C) sont homogènes, Math. Ann., 231 (1978), 217-227. Zbl0378.14003MR481133
- [15] G. Elencwajg - Des fibrés uniformes non homogènes, Preprint 1978, Nice. MR519013
- [16] D. Ferrand - Courbes gauches et fibrés de rang 2 , C. R. Acad. Sci.Paris, 281 (1975), A345-347. Zbl0315.14019MR379517
- [17] D. Gieseker - On the moduli of vector bundles on an algebraic surface, Ann. of Math., 106 (1977), 45-60. Zbl0381.14003MR466475
- [18] H. Grauert, G. Mülich - Vektorbündel vom Rang 2 über dem n-dimensionalen komplex-projektiven Raum, Manuscripta math., 16 (1975), 75-100. Zbl0318.32027MR382278
- [19] H. Grauert, R. Remmert - Zur Spaltung lokal-freier Garben über Riemannschen Flächen, Math. Z., 144 (1975), 35-43. Zbl0312.32017MR382733
- [20] H. Grauert, M. Schneider - Komplexe Unterräume und holomorphe Vektorraurnbündelvom Rang zwei, Math. Ann., 230 (1977), 75-90. Zbl0412.32014MR481134
- [21] A. Grothendieck - Sur la classification des fibrés holomorphes sur la sphère de Riemann, Amer. J. Math., 79 (1956), 121-138. Zbl0079.17001MR87176
- [22] A. Grothendieck - Théorèmes de dualité pour les faisceaux algébriques cohérents, Séminaire Bourbaki, Exposé 149, Mai 1957, W. A. Benjamin-Addison-Wesley, New York, 1966.
- [23] R. Hartshorne - Varieties of small codimension in projective space, Bull. Amer. Math. Soc., 80 (1974), 1017-1032. Zbl0304.14005MR384816
- [24] R. Hartshorne - Stable vector bundles and instantons, Comm. Math. Phys., 59 (1978), 1-15. Zbl0383.14006MR480510
- [25] R. Hartshorne - Stable vector bundles of rank 2 on P3 . Math. Ann., 238(1978), 229-280. Zbl0411.14002MR514430
- [26] R. Hartshorne - Algebraic vector bundles on projective spaces : a problem list, Preprint 1978. MR544153
- [27] G. Horrocks - Vector bundles on the punctured spectrum of a local ring, Proc. London Math. Soc. (3), 14 (1964), 689-713. Zbl0126.16801MR169877
- [28] G. Horrocks - A construction for locally free sheaves, Topology, 7 (1968), 117-120. Zbl0162.27305MR227180
- [29] G. Horrocks - Letter to Mumford (1971).
- [30] G. Horrocks - Examples of rank three vector bundles on five-dimensional projective space, J. London Math. Soc. (2), 18 (1978), 15-27. Zbl0388.14009MR502651
- [31] G. Horrocks - Construction of bundles on Pn , Preprint 1978.
- [32] G. Horrocks, D. Mumford - A rank 2 vector bundle on P4 with 15,000 symmetries, Topology, 12 (1973), 63-81. Zbl0255.14017MR382279
- [33] K. Hulek - Talk at Oberwolfach1978.
- [34] W. Hulsbergen - Vector bundles on the complex projective plane, Thesis, Leiden (1976).
- [35] S.G. Langton - Valuative criteria for families of vector bundles on algebraic varieties, Ann. of Math. (2), 101 (1975), 88-110. Zbl0307.14007MR364255
- [36] M.E. Larsen - On the topology of complex projective manifolds, Inventiones math., 19 (1973), 251-260. Zbl0255.32004MR318511
- [37] J. Le Potier - Fibrés stables de rang 2 sur P2(C) , Preprint 1978, ParisVII.
- [38] M. Maruyama - On a family of algebraic vector bundles, Number theory,algebraic geometry and commutative algebra, in honor of Y. Akizuki, Kinokuniya, Tokyo (1973), 95-146. Zbl0282.14002MR360587
- [39] M. Maruyama - Stable vector bundles on an algebraic surface, Nagoya Math. J., 58 (1975), 25-68. Zbl0337.14026MR396576
- [40] M. Maruyama - Openness of a family of torsion free sheaves, J. Math. Kyoto Univ., 16 (1976), 627-637. Zbl0404.14004MR429899
- [41] M. Maruyama - Moduli of stable sheaves, I. J. Math. Kyoto Univ., 17 (1977), 91-126. Zbl0374.14002MR450271
- [42] M. Maruyama - Moduli of stable sheaves, II. J. Math. Kyoto Univ., to appear. Zbl0395.14006MR509499
- [43] M. Maruyama - Boundedness of semi-stable sheaves of small ranks, Preprint 1978.
- [44] G. Mülich - Familien holomorpher Vektorraumbundelüber P1 und unzerlegbare holomorphe 2-Bündelüber der projektiven Ebene, Thesis, Göttingen, 1974.
- [45] A. Ogus - On the formal neighborhood of a subvariety of projective space, Amer. J. Math., 97 (1976), 1085-1107. Zbl0331.14002MR401764
- [46] E. Rees - Some rank two bundles on Pn(C) whose Chern classes vanish, In Variétés analytiques Compactes, Nice1977, Lecture Notes in Math., 683 (1978), 25-28. Zbl0384.55003MR517518
- [47] E. Sato - Uniform vector bundles on a Projective space, J. Math. Soc. Japan, 28 (1976), 123-132. Zbl0315.14003MR399101
- [48] E. Sato - On the decomposability of infinitely extendable vector bundles on projective spaces and Grassmann varieties, J. Math. Kyoto Univ., 17 (1977), 127-150. Zbl0362.14005MR437535
- [49] J.-P. Serre - Sur les modules projectifs, Séminaire Dubreil-Pisot, (1960/61), Exposé 2. Zbl0132.41301
- [50] M. Schneider - Mannigfaltigkeiten der Codimension zwei im projektiven Raum, Private Notes.
- [51] R.L.E. Schwarzenberger - Vector bundles on algebraic surfaces, Proc. London Math. Soc. (3), 11 (1961), 601-622. Zbl0212.26003MR137711
- [52] R.L.E. Schwarzenberger - Vector bundles on the projective plane, Proc. London Math. Soc. (3), 11 (1961), 623-640. Zbl0212.26004MR137712
- [53] R.L.E. Schwarzenberger - Appendix I of Topological Methods in Algebraic Geometry by F. Hirzebruch, Springer1966. MR1335917
- [54] L. Smith - Complex 2-plane bundles over CP(n) , Manuscripta Math., 24 (1978), 221-228. Zbl0383.32012MR474296
- [55] R. Switzer - Complex 2-plane bundles over complex projective space, Preprint 1978, Göttingen. MR544595
- [56] F. Takemoto - Stable vector bundles on algebraic surfaces, Nagoya Math. J.47(1972), 29-48. Zbl0245.14007MR337966
- [57] H. Tango - On (n - 1)-dimensional projective spaces contained in the Grassmann variety Gr(n,1) , J. Math. Kyoto Univ., 14 (1974), 415-460. Zbl0332.14020MR371915
- [58] H. Tango - An example of indecomposable vector bundle of rank n- 1 on Pn , J. Math. Kyoto Univ., 16(1976), 137-141. Zbl0339.14008MR401766
- [59] H. Tango - On morphisms from projective space Pn to the Grassmann variety Gr(n,d) , J. Math. Kyoto Univ., 16(1976), 201-207. Zbl0326.14015MR401787
- [60] A. Thomas - Almost complex structures on complex projective spaces, Trans. Amer. Math. Soc., 193 (1974), 123-132. Zbl0264.53019MR353196
- [61] A.N. Tjurin - Finite dimensional vector bundles over infinite varieties, Math. U.S.S.R. Isvestija10 (1976), 1187-1204.
- [62] G. Trautmann - Moduli for bundles on P n ,Preprint 1978, Kaiserslautern. MR507912
- [63] A. van de Ven - On uniform vector bundles, Math. Ann., 195(1972), 245-248. Zbl0215.43202MR291182
- [64] A. van de Ven, J. Vogelaar - A construction for vector bundles of rank 3 , Preprint 1978, Leiden.
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.