Algebraic Geometry
Atiyah–Drinfeld–Hitchin–Manin construction of framed instanton sheaves
[Construction de Atiyah–Drinfeld–Hitchin–Manin de faisceaux trivialisés d'instantons]
Comptes Rendus. Mathématique, Tome 346 (2008) no. 7-8, pp. 427-430.

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 :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2008.02.014
Jardim, Marcos 1

1 IMECC-UNICAMP, Caixa Postal 6065, 13083-859 Campinas-SP, Brazil
@article{CRMATH_2008__346_7-8_427_0,
     author = {Jardim, Marcos},
     title = {Atiyah{\textendash}Drinfeld{\textendash}Hitchin{\textendash}Manin construction of framed instanton sheaves},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {427--430},
     publisher = {Elsevier},
     volume = {346},
     number = {7-8},
     year = {2008},
     doi = {10.1016/j.crma.2008.02.014},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2008.02.014/}
}
TY  - JOUR
AU  - Jardim, Marcos
TI  - Atiyah–Drinfeld–Hitchin–Manin construction of framed instanton sheaves
JO  - Comptes Rendus. Mathématique
PY  - 2008
SP  - 427
EP  - 430
VL  - 346
IS  - 7-8
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2008.02.014/
DO  - 10.1016/j.crma.2008.02.014
LA  - en
ID  - CRMATH_2008__346_7-8_427_0
ER  - 
%0 Journal Article
%A Jardim, Marcos
%T Atiyah–Drinfeld–Hitchin–Manin construction of framed instanton sheaves
%J Comptes Rendus. Mathématique
%D 2008
%P 427-430
%V 346
%N 7-8
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2008.02.014/
%R 10.1016/j.crma.2008.02.014
%G en
%F CRMATH_2008__346_7-8_427_0
Jardim, Marcos. Atiyah–Drinfeld–Hitchin–Manin construction of framed instanton sheaves. Comptes Rendus. Mathématique, Tome 346 (2008) no. 7-8, pp. 427-430. doi : 10.1016/j.crma.2008.02.014. http://www.numdam.org/articles/10.1016/j.crma.2008.02.014/

[1] Ancona, V.; Ottaviani, G. Stability of special instanton bundles on P2n+1, Trans. Amer. Math. Soc., Volume 341 (1994), pp. 677-693

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

[3] Coandă, I.; Tikhomirov, A.; Trautmann, G. Irreducibility and smoothness of the moduli space of mathematical 5-instantons over P3, Int. J. Math., Volume 14 (2003), pp. 1-45

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

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

[6] Frenkel, I.B.; Jardim, M. Complex ADHM equations and sheaves on P3, J. Algebra, Volume 319 (2008), pp. 2913-2937

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

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

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

[10] Okonek, C.; Spindler, H. Mathematical instanton bundles on P2n+1, J. Reine Agnew. Math., Volume 364 (1986), pp. 35-50

Cité par Sources :