Noncommutative instantons and twistor transform

Communications in Mathematical Physics

Volumn 221, Issue 2, 2001, Pages 385-432

  Kapustin, Anton ^a   Kuznetsov, Alexander ^b   Orlov, Dmitri ^c  

^a INSTITUTE FOR ADVANCED STUDY   (United States)

^b INSTITUTE FOR INFORMATION TRANSMISSION PROBLEMS   (Russian Federation)

^c STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035536783     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00005576     Document Type: Article

References (40)

1. 1. Artin, M., Schelter, W.: Graded algebras of global dimension 3. Adv. Math. 66, 171-216 (1987)
2. 2. Artin, M., Tate, J., Van den Bergh, M.: Some algebras associated to automorphisms of elliptic curves. The Grothendieck Festschrift, VoL 1.. Boston: Birkhäuser, 1990, pp. 33-85
3. 3. Artin, M., Zhang, J.J.: Noncommutative projective schemes, Adv. Math. 109, no. 2, 248-287 (1994)
4. 4. Atiyah, M.F.: Geometry of Yang-Mills fields. Accademia Nationale dei Lincei, Pisa, 1979
5. 5. Atiyah, M.F., Hitchin, N.J., Drinfel'd, V.G., Manin, Yu.I.: Construction of instantons Phys. Lett. A 65, 185-187 (1978)
6. 6. Atiyah, M.F. Ward, R.S.: Instantons and Algebraic Geometry Commun. Math. Phys. 55, 117-124 (1977)
7. 7. Bando, S.: Einstein-Hermitian metrics on noncompact Kähler manifolds. In: Einstein metrics and Yang-Mills connections (Sanaa, 1990), Lecture Notes in Pure and Appl. Math. 145. New York: Dekker, 1993, pp. 27-33
8. 8. Barth, W.: Moduli of vector bundles on the projective plane Invent. Math. 42, 63-91 (1977)
9. 9. Bondal, A.I., Polishchuk, A.E.: Homological properties of associative algebras: The method of helices. Russian Acad. Sci. Izv. Math. 42, 219-260 (1994)
10. 10. Braden, H.W., Nekrasov, N.A.: Space-Time Foam from Non-Commutative Instantons. Preprint hep-th/9912019
11. 2. J. Diff. Geom. 37, 669-687 (1993)
12. 12. Connes, A.: Noncommutative Geometry. San Diego: Academic Press, 1994
13. 13. Connes, A., Douglas, M.R. and Schwarz, A.: Noncommutative Geometry and Matrix Theory: Compactification on Tori. J. High Energy Phys. 9802, 003 (1998)
14. 14. Demazure, M.: Une démonstration algébrique d'un théorème de Bott. Invent. Math. 5, 349-356 (1968)
15. 15. Donaldson, S.M.: Instantons and Geometric Invariant Theory. Commun. Math. Phys. 93, 453-460 (1984)
16. 4 and Projection Operators Preprint hep-th/9912047
17. 17. Gelfand, I.M., Shilov, G.E.: Generalized Functions vols. 1, 2. New York-London: Academic Press, 1964
18. 18. Guo, G.-Y.: On an analytic proof of a result by Donaldson. Internat. J. Math. 7, 1-17 (1996)
19. 19. Hitchin, N., Karlhede, A., Lindström, U., Roček, M.: Hyper-Kähler metrics and supersymmetry,. Commun. Math. Phys. 108, 535-589 (1987)
20. 20. Kempf, G., Ness, L.: Lengths of vectors in representation spaces. Lecture Notes in Math. 732. Berlin-New York: Springer-Verlag, 1978, pp. 233-244
21. 21. LeBruyn, L.: Moduli spaces for right ideals of the Weyl algebra. J. Algebra 172, 32-48 (1995)
22. 22. Löfwall, C.: On the subalgebra generated by one-dimensional elements in the Yoneda Ext-algebra. Lecture Notes in Math. 1183, Berlin-New York: Springer, 1986, pp. 291-338
23. 23. Lyubashenko, V.V: Hopf algebras and vector symmetries. Uspekhi Math. Nauk 41, no. 5, 185-186 (1986) (in Russian)
24. 24. Manin, Yu.I.: Gauge Field Theory and Complex Geometry. Grundlehren der mathematischen Wissenschaften 289, Berlin-New York: Springer-Verlag, 1997
25. 25. Manin, Yu.I.: Quantum groups and Noncommutative geometry. Les Publ. du Centre de Recherches Math. Montreal: Université de Montreal, 1988
26. 26. McConnell, J.C., Robson, J.C.: Noncommutative noetherian rings. Chichester: Wiley-Interscience, 1987
27. 27. Nakajima, H.: Heisenberg algebra and Hilbert schemes of points on projective surfaces, Ann. of Math. 145 no. 2, 379-388 (1997)
28. 28. Nakajima, H.: Lectures on Hilbert schemes of points on surfaces. University Lecture Series 18, Providence, RI: American Mathematical Society, 1999
29. 4 and (2, 0) superconformal six-dimensional theory. Commun. Math. Phys. 198, 689-703 (1998)
30. 30. Okonek, C., Schneider, C., Spindler, H.: Vector bundles on complex projective spaces. Boston: Birkhäuser, 1980
31. 31. Priddy, S.B.: Koszul resolutions. Trans. Am. Math. Soc. 152, 39-60 (1970)
32. 32. Seiberg, N., Witten, E.: String Theory and Noncommutative Geometry. J. High Energy Phys. 9909, 032 (1999)
33. 33. Serre, J.-P.: Faisceaux algébriques cohérents. Ann. of Math. 61, no. 2, 197-278 (1955)
34. 34. Serre, J.-P.: Modules projectifs et espaces fibrés à fibre vectorielle. Exp. 23. Paris: Séminaire Dubreil-Pisot, 1958
35. 35. Stafford, J.T., Van den Bergh, M.: Noncommutative curves and noncommutative surfaces. Preprint math.RA/9910082
36. 36. Swan, R.G.: Vector bundles and projective modules. Trans. Am. Math. Soc. 105, 264-277 (1962)
37. p} spaces. Rocky Mountain J. Math. 2, 259-263 (1972)
38. 38. Van den Bergh, M.: Existence theorem for dualizing complexes over noncommutative graded and filtered rings. J. Algebra 195, 662-679 (1997)
39. 39. Yekutieli, A.: Dualizing complexes over noncommutative graded algebras. J. Algebra 153, 41-84 (1992)
40. 40. Yekutieli, A., Zhang, J.J.: Serre duality for noncommutative projective schemes. Proc. Am. Math. Soc. 125, 697-707 (1997)