Holomorphic vector bundles on $\mathbb {P}

Holomorphic vector bundles on

ℙ_{n}

Schneider, Michael

Séminaire Bourbaki : vol. 1978/79, exposés 525-542, Séminaire Bourbaki, no. 21 (1980), Exposé no. 530, 23 p.

MR Zbl

@incollection{SB_1978-1979__21__80_0,
     author = {Schneider, Michael},
     title = {Holomorphic vector bundles on $\mathbb {P}_n$},
     booktitle = {S\'eminaire Bourbaki : vol. 1978/79, expos\'es 525-542},
     series = {S\'eminaire Bourbaki},
     note = {talk:530},
     pages = {80--102},
     publisher = {Springer-Verlag},
     number = {21},
     year = {1980},
     mrnumber = {572419},
     zbl = {0432.32016},
     language = {en},
     url = {http://archive.numdam.org/item/SB_1978-1979__21__80_0/}
}

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Schneider, Michael. Holomorphic vector bundles on $\mathbb {P}_n$, dans Séminaire Bourbaki : vol. 1978/79, exposés 525-542, Séminaire Bourbaki, no. 21 (1980), Exposé no. 530, 23 p. http://archive.numdam.org/item/SB_1978-1979__21__80_0/

Bibliographie
Cité par

[1] M.F. Atiyah, N.J. Hitchin, V.G. Drinfeld, Ju. Manin - Construction of instantons, Physics Letters, 65 A (1978), 185-187. | MR | Zbl

[2] M.F. Atiyah, E. Rees - Vector bundles on projective 3-space, Inventiones math., 35 (1976), 131-153. | MR | Zbl

[3] W. Barth - Submanifolds of low codimension in projective space, Proc. I.C.M. Vancouver (1975), 409-413. | MR | Zbl

[4] W. Barth - Some properties of stable rank -2 vector bundles on Pn , Math. Ann., 226 (1977), 125-150. | MR | Zbl

[5] W. Berth - Moduli of vector bundles on the projective plane, Inventiones math. 42 ( 1977), 63-91. | MR | Zbl

[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. | MR | Zbl

[8] W. Barth, K. Hulek - Monads and moduli of vector bundles, Manuscripta math. 25(1978), 323-347. | MR | Zbl

[9] W. Barth, A. Van De Ven - A decomposability criterion for algebraic 2-bundles on projective spaces, Inventiones Math., 25 (1974), 91-106. | MR | Zbl

[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. | MR | Zbl

[11] A. Beilinson - Coherent sheaves on PN and problems of linear algebra, J. of functional analysis and its applications, 12 (1978), 68-69. | MR | Zbl

[12] V.G. Drinfeld, Ju. Manin - On locally free sheaves over P3 connected with Yang-Mills fields, Uspechi, 33 (1978), 165-166. | MR | Zbl

[13] V.G. Drinfeld, Ju. Manin - J. Functional Analysis and its applications, 12(1978), 78-79. | Zbl

[14] G. Elencwajg - Les fibrés uniformes de rang 3 sur P2(C) sont homogènes, Math. Ann., 231 (1978), 217-227. | MR | Zbl

[15] G. Elencwajg - Des fibrés uniformes non homogènes, Preprint 1978, Nice. | MR

[16] D. Ferrand - Courbes gauches et fibrés de rang 2 , C. R. Acad. Sci. Paris, 281 (1975), A 345-347. | MR | Zbl

[17] D. Gieseker - On the moduli of vector bundles on an algebraic surface, Ann. of Math., 106 (1977), 45-60. | MR | Zbl

[18] H. Grauert, G. Mülich - Vektorbündel vom Rang 2 über dem n-dimensionalen komplex-projektiven Raum, Manuscripta math., 16 (1975), 75-100. | MR | Zbl

[19] H. Grauert, R. Remmert - Zur Spaltung lokal-freier Garben über Riemannschen Flächen, Math. Z., 144 (1975), 35-43. | MR | Zbl

[20] H. Grauert, M. Schneider - Komplexe Unterräume und holomorphe Vektorraurnbündelvom Rang zwei, Math. Ann., 230 (1977), 75-90. | MR | Zbl

[21] A. Grothendieck - Sur la classification des fibrés holomorphes sur la sphère de Riemann, Amer. J. Math., 79 (1956), 121-138. | MR | Zbl

[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. | Numdam

[23] R. Hartshorne - Varieties of small codimension in projective space, Bull. Amer. Math. Soc., 80 (1974), 1017-1032. | MR | Zbl

[24] R. Hartshorne - Stable vector bundles and instantons, Comm. Math. Phys., 59 (1978), 1-15. | MR | Zbl

[25] R. Hartshorne - Stable vector bundles of rank 2 on P3 . Math. Ann., 238(1978), 229-280. | MR | Zbl

[26] R. Hartshorne - Algebraic vector bundles on projective spaces : a problem list, Preprint 1978. | MR

[27] G. Horrocks - Vector bundles on the punctured spectrum of a local ring, Proc. London Math. Soc. (3), 14 (1964), 689-713. | MR | Zbl

[28] G. Horrocks - A construction for locally free sheaves, Topology, 7 (1968), 117-120. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[33] K. Hulek - Talk at Oberwolfach 1978.

[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. | MR | Zbl

[36] M.E. Larsen - On the topology of complex projective manifolds, Inventiones math., 19 (1973), 251-260. | MR | Zbl

[37] J. Le Potier - Fibrés stables de rang 2 sur P2(C) , Preprint 1978, Paris VII.

[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. | MR | Zbl

[39] M. Maruyama - Stable vector bundles on an algebraic surface, Nagoya Math. J., 58 (1975), 25-68. | MR | Zbl

[40] M. Maruyama - Openness of a family of torsion free sheaves, J. Math. Kyoto Univ., 16 (1976), 627-637. | MR | Zbl

[41] M. Maruyama - Moduli of stable sheaves, I. J. Math. Kyoto Univ., 17 (1977), 91-126. | MR | Zbl

[42] M. Maruyama - Moduli of stable sheaves, II. J. Math. Kyoto Univ., to appear. | MR | Zbl

[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. | MR | Zbl

[46] E. Rees - Some rank two bundles on Pn(C) whose Chern classes vanish, In Variétés analytiques Compactes, Nice 1977, Lecture Notes in Math., 683 (1978), 25-28. | MR | Zbl

[47] E. Sato - Uniform vector bundles on a Projective space, J. Math. Soc. Japan, 28 (1976), 123-132. | MR | Zbl

[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. | MR | Zbl

[49] J.-P. Serre - Sur les modules projectifs, Séminaire Dubreil-Pisot, (1960/61), Exposé 2. | Numdam | Zbl

[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. | MR | Zbl

[52] R.L.E. Schwarzenberger - Vector bundles on the projective plane, Proc. London Math. Soc. (3), 11 (1961), 623-640. | MR | Zbl

[53] R.L.E. Schwarzenberger - Appendix I of Topological Methods in Algebraic Geometry by F. Hirzebruch, Springer 1966. | MR

[54] L. Smith - Complex 2-plane bundles over CP(n) , Manuscripta Math., 24 (1978), 221-228. | MR | Zbl

[55] R. Switzer - Complex 2-plane bundles over complex projective space, Preprint 1978, Göttingen. | MR

[56] F. Takemoto - Stable vector bundles on algebraic surfaces, Nagoya Math. J. 47(1972), 29-48. | MR | Zbl

[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. | MR | Zbl

[58] H. Tango - An example of indecomposable vector bundle of rank n- 1 on Pn , J. Math. Kyoto Univ., 16(1976), 137-141. | MR | Zbl

[59] H. Tango - On morphisms from projective space Pn to the Grassmann variety Gr(n,d) , J. Math. Kyoto Univ., 16(1976), 201-207. | MR | Zbl

[60] A. Thomas - Almost complex structures on complex projective spaces, Trans. Amer. Math. Soc., 193 (1974), 123-132. | MR | Zbl

[61] A.N. Tjurin - Finite dimensional vector bundles over infinite varieties, Math. U.S.S.R. Isvestija 10 (1976), 1187-1204.

[62] G. Trautmann - Moduli for bundles on P n ,Preprint 1978, Kaiserslautern. | MR

[63] A. Van De Ven - On uniform vector bundles, Math. Ann., 195(1972), 245-248. | MR | Zbl

[64] A. Van De Ven, J. Vogelaar - A construction for vector bundles of rank 3 , Preprint 1978, Leiden.