publication . Preprint . Other literature type . 1999

Symplectic geometry on moduli spaces of holomorphic bundles over complex surfaces

Boris Khesin; Alexei Rosly;
Open Access English
  • Published: 07 Dec 1999
Abstract
Comment: 15 pages
Subjects
arXiv: Mathematics::Symplectic GeometryMathematics::Algebraic Geometry
free text keywords: Mathematics - Algebraic Geometry, High Energy Physics - Theory, Mathematics - Differential Geometry, Mathematics - Symplectic Geometry
Related Organizations
Funded by
NSERC
Project
  • Funder: Natural Sciences and Engineering Research Council of Canada (NSERC)
,
NSF| Mathematical Sciences: Basic Research in Mathematics
Project
  • Funder: National Science Foundation (NSF)
  • Project Code: 9304580
  • Funding stream: Directorate for Mathematical & Physical Sciences | Division of Mathematical Sciences
,
NSF| Mathematical Sciences: Conformal Field Theory and Its Generalizations
Project
  • Funder: National Science Foundation (NSF)
  • Project Code: 9627782
  • Funding stream: Directorate for Mathematical & Physical Sciences | Division of Mathematical Sciences
19 references, page 1 of 2

[Ar] V.I. Arnold, Arrangement of ovals of real plane algebraic curves, involutions of smooth four-dimensional manifolds, and on arithmetics of integral-valued quadratic forms, Func. Anal. and Appl. 5:3 (1971), 169-176; Remarks on eigenvalues and eigenvectors of Hermitian matrices, Berry phase, adiabatic connections and quantum Hall effect, Selecta Mathematica, New Series 1:1 (1995), 1-19.

[AB] M. Atiyah and R. Bott, The Yang-Mills equations over a Riemann surface, Philos. Trans. Roy. Soc. London 308 (1982), 523-615.

[Bot] F. Bottacin, Poisson structures on moduli spaces of sheaves over Poisson surfaces 121:2 (1995), 421-436. [OpenAIRE]

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

[DT] S.K. Donaldson and R.P. Thomas, Gauge theory in higher dimensions, The geometric universe (Oxford, 1996), Oxford Univ. Press, Oxford (1998), 31-47.

[EF] P.I. Etingof and I.B. Frenkel, Central extensions of current groups in two dimensions, Commun. Math. Phys 165 (1994), 429-444.

[FK] I.B. Frenkel and B.A. Khesin, Four-dimensional realization of two-dimensional current groups, Commun. Math. Phys 178 (1996), 541-562. [OpenAIRE]

[FR] V.V. Fock and A.A. Rosly, Poisson structures on moduli of flat connections on Riemann surfaces and r-matrices, preprint (1992); Flat connections and polyubles, Theor. Math. Phys. 95:2 (1993), 526-534.

[GS] P. Griffiths and W. Schmid, Recent developments in Hodge theory: a discussion of techniques and results, in Discrete subgroups of Lie groups and applications to moduli, Bombay Colloquium 1973, Oxford Univ. Press (1975), 31-127.

[Kh] B.A. Khesin, Informal complexification and Poisson structures on moduli spaces, AMS Transl., Ser. 2 180 (1997), 147-155. [OpenAIRE]

[Ko] S. Kobayashi, Differential geometry of complex vector bundles, Publ. Math. Soc. Japan (Iwanami Shoten and Princeton Univ. Press), 1987.

[KN] P.B. Kronheimer and H. Nakajima, Yang-Mills instantons on ALE gravitational instantons, Math. Ann. 288:2 (1990), 263-307. [OpenAIRE]

[Le] J. Leray, La calcul diff´erential et int´egral sur une vari´et´e analytique complexe (Probl´em de Cauchy, III), Bull. Soc. Math. France 87 (1959), 81-180.

[LMNS] A. Losev, G. Moore, N. Nekrasov, S. Shatashvili, Four-dimensional avatars of twodimensional RCFT, Nucl. Phys. Proc. Suppl. 46 (1996), 130-145.

[Mu] S. Mukai, Symplectic structure of the moduli space of stable sheaves on an abelian or K3 R.P. Thomas, Gauge theory on Calabi-Yau manifolds, Ph.D. thesis, Oxford (1997), 1- 104; A holomorphic Casson invariant for Calabi-Yau 3-fold, and bundles on K3 fibrations, preprint IAS (1998), 1-49.

19 references, page 1 of 2
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publication . Preprint . Other literature type . 1999

Symplectic geometry on moduli spaces of holomorphic bundles over complex surfaces

Boris Khesin; Alexei Rosly;