Atiyah–Drinfeld–Hitchin–Manin construction of framed instanton sheaves

Marcos Jardim

doi:10.1016/j.crma.2008.02.014

Algebraic Geometry

Atiyah–Drinfeld–Hitchin–Manin construction of framed instanton sheaves
[Construction de Atiyah–Drinfeld–Hitchin–Manin de faisceaux trivialisés d'instantons]

Présenté par : Christophe Soulé

Marcos Jardim ¹

¹ IMECC-UNICAMP, Caixa Postal 6065, 13083-859 Campinas-SP, Brazil

Comptes Rendus. Mathématique, Volume 346 (2008) no. 7-8, pp. 427-430.

Résumé
Abstract

Nous introduisons une généralisation de l'equation de Atiyah–Drinfeld–Hitchin–Manin que nous utilisons ensuite pour construire une classe de faisceaux sur des espaces projectifs que l'on rencontre dans le contexte de la théorie des instantons.

We introduce a generalization of Atiyah–Drinfeld–Hitchin–Manin equation, which is subsequently used to construct a class of sheaves on projective spaces that arise in connection with instanton theory.

Reçu le : 2006-12-05
Accepté le : 2008-01-29
Publié le : 2008-03-21

DOI : 10.1016/j.crma.2008.02.014

Affiliations des auteurs :

Marcos Jardim ¹

¹ IMECC-UNICAMP, Caixa Postal 6065, 13083-859 Campinas-SP, Brazil

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Marcos Jardim. Atiyah–Drinfeld–Hitchin–Manin construction of framed instanton sheaves. Comptes Rendus. Mathématique, Volume 346 (2008) no. 7-8, pp. 427-430. doi : 10.1016/j.crma.2008.02.014. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.02.014/

Bibliographie
Cité par

[1] V. Ancona; G. Ottaviani Stability of special instanton bundles on $P^{2 n + 1}$ , Trans. Amer. Math. Soc., Volume 341 (1994), pp. 677-693

[2] M. Atiyah; V. Drinfeld; N. Hitchin; Yu. Manin Construction of instantons, Phys. Lett. A, Volume 65 (1978), pp. 185-187

[3] I. Coandă; A. Tikhomirov; G. Trautmann Irreducibility and smoothness of the moduli space of mathematical 5-instantons over $P^{3}$ , Int. J. Math., Volume 14 (2003), pp. 1-45

[4] S. Donaldson Instantons and geometric invariant theory, Commun. Math. Phys., Volume 93 (1984), pp. 453-460

[5] G. Fløystad Monads on projective spaces, Comm. Algebra, Volume 28 (2000), pp. 5503-5516

[6] I.B. Frenkel; M. Jardim Complex ADHM equations and sheaves on $P^{3}$ , J. Algebra, Volume 319 (2008), pp. 2913-2937

[7] M. Jardim Instanton sheaves on complex projective spaces, Collect. Math., Volume 57 (2006), pp. 69-91

[8] M. Mamone Capria; S.M. Salamon Yang–Mills fields on quaternionic spaces, Nonlinearity, Volume 1 (1988), pp. 517-530

[9] H. Nakajima Lectures on Hilbert Schemes of Points on Surfaces, American Mathematical Society, Providence, RI, 1999

[10] C. Okonek; H. Spindler Mathematical instanton bundles on $P^{2 n + 1}$ , J. Reine Agnew. Math., Volume 364 (1986), pp. 35-50

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