Les équations de Yang-Mills. A. Douady - J.-L. Verdier - séminaire E.N.S. 1977-1978

Iliopoulos, J. ; Stora, R. ; Douady, Adrien ; Aupetit, Hubert ; Verdier, J.-L. ; Bourguignon, J.-P. ; Ferrand, Daniel ; Aupetit, Hubert ; Horrocks, Geoffrey ; Barth, Wolf ; Gruson, L. ; Peskine, C.

Avec les contributions de : Hartshorne, R.

Notes prises par : Douady, Adrien

Astérisque, no. 71-72 (1980) , 239 p.

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@book{AST_1980__71-72__1_0,
     author = {Iliopoulos, J. and Stora, R. and Douady, Adrien and Aupetit, Hubert and Verdier, J.-L. and Bourguignon, J.-P. and Ferrand, Daniel and Aupetit, Hubert and Horrocks, Geoffrey and Barth, Wolf and Gruson, L. and Peskine, C.},
     title = {Les \'equations de {Yang-Mills.} {A.} {Douady} - {J.-L.} {Verdier}  - s\'eminaire {E.N.S.} 1977-1978},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {71-72},
     year = {1980},
     language = {fr},
     url = {http://archive.numdam.org/item/AST_1980__71-72__1_0/}
}

TY  - BOOK
AU  - Iliopoulos, J.
AU  - Stora, R.
AU  - Douady, Adrien
AU  - Aupetit, Hubert
AU  - Verdier, J.-L.
AU  - Bourguignon, J.-P.
AU  - Ferrand, Daniel
AU  - Aupetit, Hubert
AU  - Horrocks, Geoffrey
AU  - Barth, Wolf
AU  - Gruson, L.
AU  - Peskine, C.
TI  - Les équations de Yang-Mills. A. Douady - J.-L. Verdier  - séminaire E.N.S. 1977-1978
T3  - Astérisque
PY  - 1980
DA  - 1980///
IS  - 71-72
PB  - Société mathématique de France
UR  - http://archive.numdam.org/item/AST_1980__71-72__1_0/
LA  - fr
ID  - AST_1980__71-72__1_0
ER  -

Iliopoulos, J.; Stora, R.; Douady, Adrien; Aupetit, Hubert; Verdier, J.-L.; Bourguignon, J.-P.; Ferrand, Daniel; Aupetit, Hubert; Horrocks, Geoffrey; Barth, Wolf; Gruson, L.; Peskine, C. Les équations de Yang-Mills. A. Douady - J.-L. Verdier  - séminaire E.N.S. 1977-1978. Astérisque, no. 71-72 (1980), Douady, Adrien (red.), 239 p. http://numdam.org/item/AST_1980__71-72__1_0/

Bibliographie
Cité par

[1] K. Wilson, P.R. D10 (1974), 2445.

[2] M. F. Atiyah, Cours à Cargèse, août 1979.

[3] G. 'T Hooft, Nuclear Physics, à paraître, où la classification des fibrés sur $T_{4}$ , est étendue au cas où le centre de $G$ n'est pas réduit à l'identité.

[4] B. Berg, M. Luscher, Desy 79/17, à paraître dans Com. Math. Phys.

[5] V. A. Faheev, I. V. Frolov, A. S. Schwarz, DESY 79/40, à paraître.

[1] J.-P. Serre, Géométrie algébrique et géometrie analytique, Annales de l'Institut Fourier, Grenoble, Tome 6, (1955-56), p. 1 à 42. | Article | EuDML 73726 | MR 82175 | Zbl 0075.30401

[1] W. Barth - Some properties of stable rank $2$ vector bundles on $ℙ_{n}$ , Math. Ann. 226 (1977) | Article | MR 429896 | Zbl 0332.32021

[2] G. Horrocks - Vector bundles on the punctured spectrum of a local ring, Proc. London Math. Soc. 14, p. 968 (1964). | MR 169877 | Zbl 0126.16801

[3] A. Douady - Le théorème des images directes, Astérisque n° 16. (exposé au Séminaire Bourbaki). | Zbl 0268.32007

[4] P. Griffiths et Adams - Topics in algebraic and analytic geometry, Princeton univ. press (1974). | MR 355119 | Zbl 0302.14003

[5] A. Grothendieck - Classification des fibrés holomorphes sur la sphère de Riemann, Ann. J. Math. 79 (1956). | MR 87176 | Zbl 0079.17001

[6] A. Grothendieck - E.G.A., ch. IV, § 5-10, I.H.E.S. n° 24 (1965).

[7] R. Hartshorne - Local cohomology, Lecture notes 41 (1967). | MR 224620

[8] M. Maruyama - Stable vector bundles on an algebraic surface, Nagoya Math. J. 58 (1975). | Article | MR 396576 | Zbl 0337.14026

[9] M. Maruyama - On a family of algebraic vector bundles, Number theory Akizuki volume - Tokio 1973. | MR 360587 | Zbl 0282.14002

[10] J. P. Serre - Faisceaux analytiques sur un espace projectif, Séminaire E.N.S. 1953-54, exp. 18-19. | EuDML 112286 | Zbl 0119.06802

[11] J. P. Serre - F.A.C.

[12] Van De Ven - On uniform vector bundles, Math. Ann. 195 (1971). | Article | EuDML 162227 | MR 291182 | Zbl 0215.43202

[1] A. A. Beylinson. Coherent sheaves on $ℙ^{M}$ and problems of linear algebra, Funktional Anal. 12, vol. 1978. | MR 509388 | Zbl 0424.14003

[2] V. G. Drinfel'D and Ju. I. Manin. Instantons and sheaves on ${ℂℙ}^{3}$ , Proceedings of Copenhagen Summer Meeting in Algebraic Geometry, Springer Lecture Notes. To appear. | MR 555691 | Zbl 0412.14020

[3] D. Mumford. Geometric Invariant Theory, Ergebuisse, Springer-Verlag, 1965. | MR 214602 | Zbl 0147.39304

[1] M. Atiyah, R. Bott, P. Shapiro - Clifford modules, Topology suppl. vol. 3 (1964). | MR 167985 | Zbl 0146.19001

[2] M. Atiyah, N. Hitchin, I. M. Singer - Self duality in four dimensional Riemannian geometry, Proc. R. Soc. Lond., A362 (1978), 425-461. | Article | MR 506229 | Zbl 0389.53011

[3] J. P. Bourguignon - Riemannian geometry, differential operators and elementary representations theory, à paraître.

[4] J. P. Bourguignon, H. B. Lawson, J. Simons - Stability and gap phenomena for Yang-Mills fields, Proc. Nat. Acad. Sci. U.S.A., (1979) | MR 526178 | Zbl 0408.53023

[5] N. Hitchin - Harmonic spinors, Adv. in Math., n° 14, (1974). | MR 358873 | Zbl 0284.58016

[6] S. Kirillov - Éléments de la théorie des représentations, Mir, Moscou (1972). | MR 393324

[7] A. Lichnerowicz - Spineurs harmoniques, Note aux C.R.A.S. Paris, t. 257 (1963), 7-9. | MR 156292 | Zbl 0136.18401

[8] R. S. Palais - Seminar on the Atiyah-Singer index theorem, Princeton Math. Studies, n° 57 (1965). | MR 198494 | Zbl 0137.17002

[9] P. Stredder - Natural differential operators on Riemannian manifolds and representations of the orthogonal and special orthogonal groups, J. of Diff. Geom., 10 (1975), 647-660. | Article | MR 415692 | Zbl 0318.53046

[1] A. Altman et S. Kleiman" - Introduction to Grothendieck duality theory, Lecture Notes in Math., n° 146, Springer-Verlag, 1970. | MR 274461 | Zbl 0215.37201

[2] D. Ferrand - Suites régulières et intersections complètes, Notes aux C.R.A.S. de Paris, t. 264, (6 Mars 1967). | MR 219546 | Zbl 0154.03801

[3] D. Ferrand - Courbes gauches et fibres de rang deux, Note aux C.R.A.S. de Paris, t. 281 (8 Sept, 1975). | MR 379517 | Zbl 0315.14019

[4] A. Grothendieck - Fondements de la géometrie algébrique. | Zbl 0239.14001

[5] G. Horhocks - A construction for locally free sheaves, Topology, vol. 7 (1968). | MR 227180 | Zbl 0162.27305

[6] A. Micali - Sur les algèbres universelles, Ann. Inst. Fourier (1964). | EuDML 73843 | MR 177009 | Zbl 0152.02602

[7] R. L. E. Schwarzenberger - Vector bundles on algebraic surfaces, Proc. London Math. Soc. 1961. | MR 137711 | Zbl 0212.26003

[8] J.-P. Serre - Sur les modules projectifs. Seminaire Dubreil-Pisot, 1960/61. | EuDML 111203 | Zbl 0132.41301

[1] M. F. Atiyah, E. Rees - Vector bundles on projective $3$ -space, Inv. Math. 35, 131-153 (1976). | Article | EuDML 142403 | MR 419852 | Zbl 0332.32020

[2] W. Barth, G. Elencwajg - Concernant la cohomologie des fibrés algébriques stables sur $ℙ_{n} (ℂ)$ . In : Variétés analytiques compactes, Nice (1977). | Zbl 0381.55005

[3] W. Barth, K. Hulek - Monads and moduli of vector bundles, to appear. | Article | MR 509589 | Zbl 0395.14007

[4] A. A. Beilinson - Coherent sheaves on $ℙ_{n}$ and problems of linear algebra. Preprint (1978). | MR 509388 | Zbl 0424.14003

[5] G. Horrocks - Construction of bundles on $ℙ_{n}$ . This seminar (1977).

[1] W. Barth - Some properties of stable rank- $2$ vector bundles on ${\overset{P}{=}}_{n}$ , Math. Ann., 226 (1977), pp. 125-150. | Article | EuDML 162947 | MR 429896 | Zbl 0332.32021

[2] Bourbaki - Algèbre, chapitre III (ancienne édition). | Article | MR 26989

[3] G. Castelnuovo - Sui multipli di una serie lineare di gruppi di punti..., Rendiconti Cire. mat. Palermo, 7 (1893), pp. 89-110. | Article | JFM 25.1035.02

[4] F. R. Gantmacher - Matrizenrechnung, t. 2, VEB Verlag der Wissenschaften. | MR 279108 | Zbl 0079.01106

[5] L. Gruson et C. Peskine - Genre des courbes de l'espace projectif, Proc. Tromsø conference on alg. geom., 1977, à paraître (Lecture notes, Springer). | MR 527229 | Zbl 0412.14011

[6] G. H. Halphen - Mémoire sur la classification des courbes gauches algébriques, Oeuvres complètes, t. III, pp. 261-455.

[7] J. Harris - Thesis, Harvard University, 1977 (preprint).

[8] O. A. Laudal - A generalized trisecant lemma, Proc. Tromsø conference on algebraic geometry, 1977, à paraître (Lectures notes, Springer) | MR 527232 | Zbl 0392.14002

[9] Th. Muir - A treatise on the theory of determinants, Dover. | JFM 15.0118.05 | MR 114826

[10] D. Mumford - Curves on algebraic surfaces, Annals of math. studies n° 59, Princeton. | Zbl 0187.42701

[11] C. Peskine et L. Szpiro - Liaison des variétés algébriques, Inv. math. 26 (1973), pp. 271-302. | Article | EuDML 142303 | MR 364271 | Zbl 0298.14022

M. F. Atiyah, Geometry of Yang-Mills fields, Proc. International Conf. Math. Physics, Rome (1976). | Zbl 0435.58001

Mf. Atiyah, V. G. Drinfeld, N. J. Hitchin and Yu. I. Manin, Construction of Instantons, Phys. Lett. 65 A, n° 3 (1978), 185-187. | Article | MR 598562 | Zbl 0424.14004

M. F. Atiyah, N. Hitchin and I. M. Singer, Deformations of instantons, Proc. Nat. Acad. Sci. 74 (1977), 2662-2663. | Article | MR 458424 | Zbl 0356.58011

M. F. Atiyah, N. Hitchin and J. M. Singer, Self-duality in four-dimensional Riemannian Geometry, Proc. Roy. Soc. (to appear). | MR 506229 | Zbl 0389.53011

M. F. Atiyah, and J.S.D. Jones, Topological aspects of Yang-Mills theory (to appear). | MR 503187 | Zbl 0387.55009

M. F. Atiyah and E. Rees, Vector bundles on projective 3-space, Invent. Math., 35, (1976) , 131-153. | Article | EuDML 142403 | MR 419852 | Zbl 0332.32020

M. F. Atiyah and R. Ward, Instantons and algebraic geometry, Commun. Math. Phys. 55, (1977), 117-124. | Article | MR 494098 | Zbl 0362.14004

W. Barth, Some properties of stable rank- $2$ vector bundles on $ℙ_{n}$ , Math. Ann. 226, (1977), 125-150. | Article | EuDML 162947 | MR 429896 | Zbl 0332.32021

W. Barth, Moduli of vector bundles on the projective plane, Invent. Math. 42, (1977) , 63-91. | Article | EuDML 142496 | MR 460330 | Zbl 0386.14005

W. Barth and K. Hulek, Monads and Moduli of vector bundles, Manusc. Math. 25, (1978) , 323-347. | Article | EuDML 154571 | MR 509589 | Zbl 0395.14007

W. Barth and A. Van De Ven, A decomposability criterion for algebraic $2$ -bundles on projective spaces, Invent. Math. 25, (1974), 91-106. | Article | EuDML 142283 | MR 379515 | Zbl 0295.14006

W. Barth and A. Van De Ven, On the geometry in codimension $2$ of Grassmann manifolds, in "Classification of Algebraic Varieties and Compact Complex Manifolds", Lecture Notes in Math. 412, Springer-Verlag, Heidelberg, New-York, (1974), 1-35. | Article | MR 354661 | Zbl 0299.14024

A. A. Belavin, A. M. Poliakov, A. S. Schwartz, Yu. Tyupkin, Pseudoparticle solutions of the Yang-Mills equations, Phys. Lett., B 59 n° 1 , (1975), 85-87. | Article | MR 434183

A. A. Belavin, V. E. Zakharov, JEPT Letters, 25 : 12 (1977), 603-607.

C. W. Bernard, N. H. Christ, A. H. Guth, E. J. Weinberg, Instanton parameters for arbitrary gauge groups, (Preprint CU-TP-105, Columbia University, 1977). | MR 459426

I. N. Bernshtein, I. M. Gelfand, S. I. Gelfand, Algebraic bundles over $ℙ_{n}$ and problems of linear algebra, Funkcional Anal., 12, Vol. 3, (1978). | Zbl 0402.14005

A. A. Beilinson, Coherent sheaves on $ℙ_{n}$ and problems of linear algebra, Funkcional Anal. 12, Vol. 3, (1978). | MR 509388 | Zbl 0402.14006

J. P. Bourguignon, H. B. Lawson and J. Simons, Stability and Gap Phenomena for Yang-Mills Fields, (à paraître). | Article | Zbl 0408.53023

C. G. Calian, R. Dashen and D. J. Gross, Toward a theory of the strong interactions (Preprint COO - 2220-115, 1977).

E. F. Corrigan, D. B. Fairlic, R. C. Yates and P. Goddard, The construction of self-dual solution to $S U (2)$ Gauge theory, Commun. Math. Phys., 58, (1978), 223-240. | Article | MR 475358

V. G. Drinfeld and Yu. I Manin, A description of instantons, (Preprint N 72, 1978). | MR 513898 | Zbl 0407.22017

V. G. Drinfeld and Yu. I. Manin, Self-dual Yang-Mills fields on the sphere, Funkcional Anal. 12, Vol. 2, (1978), 78-89. | MR 500956 | Zbl 0402.53040

V. G. Drinfeld and Yu. I. Manin, On locally free sheaves on ${ℂℙ}^{3}$ associated with the Yang-Mills fields, UMN (Translated as Russian Math. Surveys), Vol. 2, (1978), 241-242.

V. G. Drinfeld and Yu. I. Manin, Instantons and sheaves on ${ℂℙ}^{3}$ , à paraître dans Proceedings of Copenhagen Summer Meeting in Algebraic Geometry, Springer, Lecture Notes. | MR 555691 | Zbl 0412.14020

G. Elenewajg, Les fibrés uniformes de rang $3$ sur $ℙ_{2} (ℂ)$ sont homogènes, Math. Ann. 231, (1978), 217-227. | Article | EuDML 163062 | MR 481133 | Zbl 0378.14003

D. Ferrand, Courbes gauches et fibrés de rang $2$ , C.R. Acad. Sci. Paris, 281, (1975), A 345-547. | MR 379517 | Zbl 0315.14019

D. Gieseker, On the moduli of vector bundles on an algebraic surface, Annals of Math., 106, (1977), 45-60. | Article | MR 466475 | Zbl 0381.14003

H. Grauert, H. and G. Mülich, Vektorbündel vom Rang $2$ über dem $n$ -dimensionalen Komplex-projectiven Raum, Manusc. Math., 16, (1975), 75-100. | Article | EuDML 154335 | MR 382278 | Zbl 0318.32027

R. Hartshorne, A property of $A$ -sequences, Bull. Soc. Math. France, 94, (1966), 61-66. | Article | EuDML 87089 | MR 209279 | Zbl 0142.28605

R. Hartshorne, Varieties of small codimension in projective space, Bull. AMS, 80, (1974), 1017-1032. | Article | MR 384816 | Zbl 0304.14005

R. Hartshorne, The classification of curves in $ℙ^{3}$ and related topics (Lecture Notes in Japanese by M. Ishida and E. Sato), Math. Res. Lec. Notes, 2 Kyoto Univ., (1977), 74 pp.

R. Hartshorne, Algebraic Geometry, Graduate Texts in Math., 52, Springer-Verlag, Heidelberg, New-York, (1977), xvi + 496 pp. | Article | MR 463157 | Zbl 0531.14001

R. Hartshorne, Stable vector bundles and instantons, Commun. Math. Physics (to appear). | MR 480510 | Zbl 0383.14006

R. Hartshorne, Stable vector bundles of rank $2$ on $ℙ^{3}$ . | Zbl 0411.14002

G. Horrocks, Vector bundles on the punctured spectrum of a local ring, Proc. London Math. Soc., 14, (1964), 689-713. | Article | MR 169877 | Zbl 0126.16801

G. Horrocks, A construction for locally free sheaves, Topology I, (1968) 117-120. | Article | MR 227180 | Zbl 0162.27305

G. Horrocks, Examples of rank three vector bundles on five dimensional projective space, (Preprint). | MR 502651 | Zbl 0388.14009

G. Horrocks and D. Mumford, A rank $2$ vector bundles on $ℙ^{4}$ with 15,000 symmetries, Topology, 12, (1973), 63-81. | Article | MR 382279 | Zbl 0255.14017

S. L. Kleiman, Geometry on Grassmannians and applications to splitting bundles and smoothing cycles, Publ. Math. IHES, 36, (1969), 281-298. | Article | EuDML 103895 | MR 265371 | Zbl 0208.48501

J. Le Potier, Fibrés stables de rang $2$ sur $ℙ_{2} (ℂ)$ . | Zbl 0405.14008

M. Maruyama, On a family of algebraic vector bundles (in) Number Theory, Algebraic Geometry, and Commutative Algebra, in honor of Y. Akisuki, Kinokuniya, Tokyo, (1965), 95-146. | MR 360587 | Zbl 0282.14002

M. Maruyama, Stable vector bundles on an algebraic surface, Nagoya Math. J., 58, (1975), 25-68. | Article | MR 396576 | Zbl 0337.14026

M. Maruyama, Opennes of a family of torsion free sheaves, J. Math. Kyoto Univ., 16, (1976), 627-637. | Article | MR 429899 | Zbl 0404.14004

M. Maruyama, Moduli of stable sheaves, I, J. Math. Kyoto Univ., 17, (1977), 91-126. | Article | MR 450271 | Zbl 0374.14002

M. Maruyama, Moduli of stable sheaves, II, (Preprint). | Article | Zbl 0395.14006

D. Mumford, Lectures on curves on an algebraic surface, Annals of Math. Studies, 59, Princeton Univ. Press. Princeton, (1966), 200 pp. | MR 209285 | Zbl 0187.42701

D. Mumford, Varieties defined by quadratic equations, (with an Appendix by G. Kempf) in Questions on Algebraic Varieties, C.I.M.E. ed. Cremonese, Rome, (1970), 29-100. | MR 282975 | Zbl 0198.25801

D. Mumford, Theta Characteristics of an algebraic curve, Ann. Sc. ENS, 4, (1971), 181-192. | EuDML 81878 | MR 292836 | Zbl 0216.05904

M. S. Narasimhan and C. S. Seshadri, Stable and unitary vector bundle on a compact Riemann Surface, Annals of Math., 82, (1965), 540-567. | Article | MR 184252 | Zbl 0171.04803

C. Peskine and L. Szpiro, Liaison des variétés algébriques (I), Invent. Math., 26, (1974), 271-502. | Article | EuDML 142303 | MR 364271 | Zbl 0298.14022

A. M. Polyakov, Compact Gauge fields and the infrared catastrophe, Phys. Lett. 59B n° 1, (1975), 82-84. | Article

A. M. Polyakov, Interaction of Goldstone particles in two dimensions. Application to ferromagnets and massive Yang-Mills, Phys. Lett. 59B n° 1, (1975), 79-80. | Article

A. P. Rao, Liaison among curves in $ℙ^{3}$ , (Preprint). | MR 520926 | Zbl 0406.14033

B. Saint-Donnat, On Petri's analysis of the linear system of quadrics through a canonical curve, Math. Ann., 206, (1965), 157-175. | Article | EuDML 162512 | MR 337983 | Zbl 0315.14010

E. Sato, On the decomposability of infinitely extendable vector bundles on projective spaces and Grassmann varieties, J. Math., Kyoto Univ., 17, (1977), 127-150. | Article | MR 437535 | Zbl 0362.14005

E. Sato, The decomposability of an infinitely extendable vector bundle on the projective space, II, (Preprint). | MR 578879 | Zbl 0405.14011

E. Sato, On infinitely extendable vector bundles on $G / P$ , (Preprint). | MR 527401 | Zbl 0423.14034

A. S. Schwartz, Phys. Lett., 67B, (1977), 172-174. | Article

J.-P. Serre, Sur les modules projectifs, Séminaire Dubreil-Pisot (1960/61), Secr. Math. Paris (1961), exposé 2. | EuDML 111203 | Zbl 0132.41301

R. Stora, Yang-Mills instantons, geometrical aspects, (Preprint 77/P. 945, Centre de Physique Théorique, CNRS). | Article | MR 523207

F. Takemoto, Stable vector bundles on algebraic surfaces, Nagoya Math. J., 47, (1972). | Article | MR 337966 | Zbl 0245.14007

H. Tango, On morphisms from the projective space $ℙ^{n}$ to the Grassmann variety Gr(n,d), (Preprint). | MR 401787 | Zbl 0642.14012

G. Trautmann, Moduli for vector bundles on $ℙ_{n} (ℂ)$ , Math. Annal. 257, (1978), 167-186. | EuDML 182784 | MR 507912 | Zbl 0369.32009

A. N. Tyurin, Finite dimensional vector bundles over infinite varieties, (Preprint). | MR 2742585

G. P. Wever, The moduli of a class of rank $2$ vector bundles on projective $3$ spaces, thesis, Univ. Calif. Berkeley, (1977).

E. Witten, Some exact multi instanton solutions of classical Yang-Mills theory, (Preprint Harvard).