Integrable systems and algebraic surfaces

previous :: next

Integrable systems and algebraic surfaces

J. C. Hurtubise

Source: Duke Math. J. Volume 83, Number 1 (1996), 19-50.

First Page: Show

Related Works:

See also: Jacques Hurtubise. Erratum to the paper “Integrable systems and algebraic surfaces,” vol. 83 (1996) pp. 19–50. Duke Math. J. Vol. 84, No. 3 (1996), pp. 815–815.

Project Euclid: euclid.dmj/1077244044

Primary Subjects: 14H40

Secondary Subjects: 14J25, 17B65, 58F07

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.

If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077244246
Mathematical Reviews number (MathSciNet): MR1408545
Zentralblatt MATH identifier: 0857.58024
Digital Object Identifier: doi:10.1215/S0012-7094-96-08302-7

back to Table of Contents

References

[AHH1] M. R. Adams, J. Harnad, and J. Hurtubise, Isospectral Hamiltonian flows in finite and infinite dimensions II. Integration of flows, Comm. Math. Phys. 134 (1990), no. 3, 555–585.

Mathematical Reviews (MathSciNet): MR92a:58055

Zentralblatt MATH: 0717.58051

Digital Object Identifier: doi:10.1007/BF02098447

Project Euclid: euclid.cmp/1104201822

[AHH2] M. R. Adams, J. Harnad, and J. Hurtubise, Darboux coordinates and Liouville-Arnold integration in loop algebras, Comm. Math. Phys. 155 (1993), no. 2, 385–413.

Mathematical Reviews (MathSciNet): MR94j:58071

Zentralblatt MATH: 0791.58047

Digital Object Identifier: doi:10.1007/BF02097398

Project Euclid: euclid.cmp/1104253285

[AHH3] M. R. Adams, J. Harnad, and J. Hurtubise, Darboux coordinates and Serre duality, CRM preprint, 1994.

[AHH4] M. R. Adams, J. Harnad, and J. Hurtubise, Coadjoint Orbits, Spectral Curves and Darboux Coordinates, The Geometry of Hamiltonian Systems (Berkeley, CA, 1989) ed. T. Ratiu, Publ. MSRI, vol. 22, Springer-Verlag, New York, 1991, pp. 9–21.

Mathematical Reviews (MathSciNet): MR92k:58095

Zentralblatt MATH: 0739.58014

[AHP] M. R. Adams, J. Harnad, and E. Previato, Isospectral Hamiltonian flows in finite and infinite dimensions I. Generalized Moser systems and moment maps into loop algebras, Comm. Math. Phys. 117 (1988), no. 3, 451–500.

Mathematical Reviews (MathSciNet): MR89k:58112

Zentralblatt MATH: 0659.58022

Digital Object Identifier: doi:10.1007/BF01223376

Project Euclid: euclid.cmp/1104161743

[AvM1] M. Adler and P. van Moerbeke, Kowalewski's asymptotic method, Kac-Moody Lie algebras and regularization, Comm. Math. Phys. 83 (1982), no. 1, 83–106.

Mathematical Reviews (MathSciNet): MR83c:58036

Zentralblatt MATH: 0491.58017

Digital Object Identifier: doi:10.1007/BF01947073

Project Euclid: euclid.cmp/1103920747

[AvM2] M. Adler and P. van Moerbeke, The complex geometry of the Kowalewski-Painlevé analysis, Invent. Math. 97 (1989), no. 1, 3–51.

Mathematical Reviews (MathSciNet): MR90f:58079

Zentralblatt MATH: 0678.58020

Digital Object Identifier: doi:10.1007/BF01850654

[AvM3]¹ M. Adler and P. van Moerbeke, Completely integrable systems, Euclidean Lie algebras, and curves, Adv. in Math. 38 (1980), no. 3, 267–317.

Mathematical Reviews (MathSciNet): MR83m:58041

Zentralblatt MATH: 0455.58017

Digital Object Identifier: doi:10.1016/0001-8708(80)90007-9

[AvM3]² M. Adler and P. van Moerbeke, Linearization of Hamiltonian systems, Jacobi varieties and representation theory, Adv. in Math. 38 (1980), no. 3, 318–379.

Mathematical Reviews (MathSciNet): MR83m:58042

Zentralblatt MATH: 0455.58010

Digital Object Identifier: doi:10.1016/0001-8708(80)90008-0

[A] V. I. Arnold, Mathematical Methods of Classical Mechanics, Springer Verlag, Berlin, 1978.

Mathematical Reviews (MathSciNet): MR57:14033b

Zentralblatt MATH: 0386.70001

[BPV] W. Barth, C. Peters, and A. Van de Ven, Compact Complex Surfaces, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 4, Springer Verlag, Berlin, 1984.

Mathematical Reviews (MathSciNet): MR86c:32026

Zentralblatt MATH: 0718.14023

[B] A. Beauville, Jacobiennes des courbes spectrales et systèmes hamiltoniens complètement intégrables, Acta Math. 164 (1990), no. 3-4, 211–235.

Mathematical Reviews (MathSciNet): MR91m:14044

Zentralblatt MATH: 0712.58031

Digital Object Identifier: doi:10.1007/BF02392754

[B2] A. Beauville, Variétés Kähleriennes dont la première classe de Chern est nulle, J. Differential Geom. 18 (1983), no. 4, 755–782 (1984).

Mathematical Reviews (MathSciNet): MR86c:32030

Zentralblatt MATH: 0537.53056

Project Euclid: euclid.jdg/1214438181

[BCGGG] R. L. Bryant, S. S. Chern, R. B. Gardner, H. L. Goldschmidt, and P. A. Griffiths, Exterior Differential Systems, MSRI Publications, vol. 18, Springer-Verlag, New York, 1991.

Mathematical Reviews (MathSciNet): MR92h:58007

Zentralblatt MATH: 0726.58002

[C] W. L. Chow, On compact complex analytic varieties, Amer. J. Math. 71 (1949), 893–914.

Mathematical Reviews (MathSciNet): MR11,389f

Zentralblatt MATH: 0041.48302

Digital Object Identifier: doi:10.2307/2372375

JSTOR: links.jstor.org

[DM] R. Donagi and E. Markman, Cubics, integrable systems and Calabi-Yau three-folds, Proceedings of the Hirzebruch 65 Conference on Algebraic Geometry (Ramat Gan, 1993), Israel Mathematical Conference Proceedings, vol. 9, Bar-Ilan Univ., Ramat Gan, 1996, pp. 199–221.

Mathematical Reviews (MathSciNet): MR97f:14039

Zentralblatt MATH: 0878.14031

[FK] H. M. Farkas and I. Kra, Riemann Surfaces, Graduate Texts in Math., vol. 71, Springer, New York, 1980.

Mathematical Reviews (MathSciNet): MR82c:30067

Zentralblatt MATH: 0475.30001

[F] J. Fogarty, Algebraic families on an algebraic surface, Amer. J. Math 90 (1968), 511–521.

Mathematical Reviews (MathSciNet): MR38:5778

Zentralblatt MATH: 0176.18401

Digital Object Identifier: doi:10.2307/2373541

JSTOR: links.jstor.org

[FRS] I. B. Frenkel, A. G. Reiman, and M. A. Semenov-Tian-Sansky, Graded Lie algebras and completely integrable dynamical systems, Dokl. Akad. Nauk SSSR 247 (1979), no. 4, 802–805.

Mathematical Reviews (MathSciNet): MR81c:58042

Zentralblatt MATH: 0437.58008

[GH] P. Griffiths and J. Harris, Principles of Algebraic Geometry, Wiley, New York, 1978.

Mathematical Reviews (MathSciNet): MR80b:14001

Zentralblatt MATH: 0408.14001

[HH] J. Harnad and J. Hurtubise, Generalized tops and moment maps to loop algebras, J. Math. Phys. 32 (1991), no. 7, 1780–1787.

Mathematical Reviews (MathSciNet): MR92m:58060

Zentralblatt MATH: 0733.70012

Digital Object Identifier: doi:10.1063/1.529241

[Hi1] N. J. Hitchin, The self-duality equations on a Riemann surface, Proc. London Math. Soc. (3) 55 (1987), no. 1, 59–126.

Mathematical Reviews (MathSciNet): MR89a:32021

Zentralblatt MATH: 0634.53045

Digital Object Identifier: doi:10.1112/plms/s3-55.1.59

[Hi2] N. J. Hitchin, Stable bundles and integrable systems, Duke Math. J. 54 (1987), no. 1, 91–114.

Mathematical Reviews (MathSciNet): MR88i:58068

Zentralblatt MATH: 0627.14024

Digital Object Identifier: doi:10.1215/S0012-7094-87-05408-1

Project Euclid: euclid.dmj/1077305506

[H] J. C. Hurtubise, Finite-dimensional coadjoint orbits in loop algebras, Lett. Math. Phys. 30 (1994), no. 2, 99–104.

Mathematical Reviews (MathSciNet): MR95c:22026

Zentralblatt MATH: 0797.17015

Digital Object Identifier: doi:10.1007/BF00939697

[HK] J. C. Hurtubise and N. Kamran, Projective connections, double fibrations, and formal neighbourhoods of lines, Math. Ann. 292 (1992), no. 3, 383–409.

Mathematical Reviews (MathSciNet): MR93f:32033

Zentralblatt MATH: 0738.58051

Digital Object Identifier: doi:10.1007/BF01444628

[I] A. Iarrobino, Hilbert scheme of points: overview of last ten years, Algebraic geometry, Bowdoin, 1985 (Brunswick, Maine, 1985), Proc. Sympos. Pure Math. (2), vol. 46, Amer. Math. Soc., Providence, RI, 1987, pp. 297–320.

Mathematical Reviews (MathSciNet): MR89b:14007

Zentralblatt MATH: 0646.14002

[Kr] I. M. Krichever, Methods of algebraic geometry in the theory of nonlinear equations, Russian Math. Surveys 32 (1977), 185–213.

Zentralblatt MATH: 0386.35002

Mathematical Reviews (MathSciNet): MR516323

[KrN] I. M. Krichever and S. P. Novikov, Holomorphic bundles over algebraic curves and nonlinear equations, Russian Math. Surveys 32 (1980), 53–79.

Zentralblatt MATH: 0548.35100

Mathematical Reviews (MathSciNet): MR601756

[M] S. Mukai, Symplectic structure of the moduli space of sheaves on an abelian or $K-3$ surface, Invent. Math. 77 (1984), no. 1, 101–116.

Mathematical Reviews (MathSciNet): MR85j:14016

Zentralblatt MATH: 0565.14002

Digital Object Identifier: doi:10.1007/BF01389137

[RS]¹ A. G. Reyman and M. A. Semenov-Tian-Shansky, Reduction of Hamiltonian systems, affine Lie algebras and Lax equations, Invent. Math. 54 (1979), no. 1, 81–100.

Mathematical Reviews (MathSciNet): MR81b:58021

Zentralblatt MATH: 0403.58004

Digital Object Identifier: doi:10.1007/BF01391179

[RS]² A. G. Reyman and M. A. Semenov-Tian-Shansky, Reduction of Hamiltonian systems, affine Lie algebras and Lax equations II, Invent. Math. 63 (1981), no. 3, 423–432.

Mathematical Reviews (MathSciNet): MR82k:58049

Zentralblatt MATH: 0442.58016

Digital Object Identifier: doi:10.1007/BF01389063

[S] E. K. Sklyanin, Separation of variables in the classical integrable $\rm SL(3)$ magnetic chain, Comm. Math. Phys. 150 (1992), no. 1, 181–191.

Mathematical Reviews (MathSciNet): MR93k:82020

Zentralblatt MATH: 0764.35106

Digital Object Identifier: doi:10.1007/BF02096572

Project Euclid: euclid.cmp/1104251789

[Sc] D. R. D. Scott, Classical functional Bethe ansatz for $\rm SL(N)$: separation of variables for the magnetic chain, J. Math. Phys. 35 (1994), no. 11, 5831–5843.

Mathematical Reviews (MathSciNet): MR95j:82021

Zentralblatt MATH: 0822.58029

Digital Object Identifier: doi:10.1063/1.530712

[vM] P. van Moerbeke, Introduction to algebraic integrable systems and their Painlevé analysis, Theta functions—Bowdoin 1987, Part 1 (Brunswick, ME, 1987), Proc. Sympos Pure Math., vol. 49, Amer. Math. Soc., Providence, RI, 1989, pp. 107–131.

Mathematical Reviews (MathSciNet): MR91a:58084

Zentralblatt MATH: 0688.70012

previous :: next

Duke Mathematical Journal

Turn MathJax Off
What is MathJax?