A special case of the Garnier system, (1,4)-polarized abelian surfaces and their moduli
Vanhaecke, Pol
Compositio Mathematica, Tome 94 (1994), p. 157-203 / Harvested from Numdam
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Publié le : 1994-01-01
@article{CM_1994__92_2_157_0,
     author = {Vanhaecke, Pol},
     title = {A special case of the Garnier system, $(1, 4)$-polarized abelian surfaces and their moduli},
     journal = {Compositio Mathematica},
     volume = {94},
     year = {1994},
     pages = {157-203},
     mrnumber = {1283227},
     zbl = {0851.58026},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1994__92_2_157_0}
}

Vanhaecke, Pol. A special case of the Garnier system, $(1, 4)$-polarized abelian surfaces and their moduli. Compositio Mathematica, Tome 94 (1994) pp. 157-203. http://gdmltest.u-ga.fr/item/CM_1994__92_2_157_0/

[A] Arnold, V.: Mathematical Methods of Classical Mechanics. Springer-Verlag (1978). | MR 690288 | Zbl 0386.70001

[AvM1] Adler, M., Van Moerbeke, P.: Algebraic completely integrable systems: a systematic approach. Perspectives in Mathematics, Academic Press (to appear in 1995).

[AvM2] Adler, M., Van Moerbeke, P., Representing the Kowalevski and Henon-Heiles motions as Manakov geodesic flows on SO(4) and a two-dimensional family of Lax pairs, Commun. Math. Phys., 114, 1-41 (1987).

[AvM3] Adler, M., Van Moerbeke, P., The complex geometry of the Kowalewski-Painlevé analysis, Invent. Math., 97, 3-51 (1987). | MR 999312 | Zbl 0678.58020

[B] Baltuch, J.: Integrable systems and reducible Abelian surfaces of type (1,2). Doctoral thesis at Brandeis University, 1991.

[Ba] Barth, W.: Abelian surfaces with (1, 2) polarization, Conference on Algebraic Geometry, Sendai (1985). | Zbl 0639.14023

[Be] Beauville, A., Jacobiennes des courbes spectrales et systèmes hamiltoniens complètement intégrables, Acta Math., 164, 211-235 (1990). | MR 1049157 | Zbl 0712.58031

[BLS] Birkenhake, C., Lange, H., Van Straten, D., Abelian surfaces of type (1,4), Math. Ann., 285, 625-646 (1989). | MR 1027763 | Zbl 0714.14028

[Bu] Bueken, P.: A geodesic flow on SO(4) and Abelian surfaces of type (1, 4). (Preprint).

[CC] Chudnovsky, D.V., Chudnovsky, G.V., A completely integrable class of mechanical systems connected with Korteweg-de Vries and multicomponent Schrödinger equations, Lett. Nuovo Cim., 22/4, 47-51 (1978). | MR 497773

[D] Dubrovin, B.A., Theta functions and nonlinear equations, Russian Math. Surveys, 36/2, 11-92 (1982). | MR 616797 | Zbl 0549.58038

[F] Flaschka, H., Monodromy- and Spectrum-Preserving Deformations I, Commun. Math. Phys., 76, 65-116 (1980). | MR 588248 | Zbl 0439.34005

[G] Garnier, R., Sur une classe de systèmes différentiels abéliens déduits de théorie des équations linéaires, Rend. Circ. Math. Palermo, 43/4, 155-191 (1919). | JFM 47.0404.01

[Gr] Griffiths, P.A., Linearizing flows and a cohomological interpretation of Lax equations, Am. J. of Math., 107, 1445-1483 (1985). | MR 815768 | Zbl 0585.58028

[GH] Griffiths, P. and Harris, J.: Principles of Algebraic Geometry. Wiley-Interscience, New York (1978). | MR 507725 | Zbl 0408.14001

[Hu] Hudson, R.W.H.: Kummer's quartic surface. Cambridge: Cambridge University Press (1990); first published in 1905. | JFM 36.0709.03 | MR 1097176 | Zbl 0716.14025

[LB] Lange, H., Birkenhake, C.: Complex Abelian Varieties. Springer-Verlag (1992). | MR 1217487 | Zbl 0779.14012

[M1] Mumford, D., On the equations defining Abelian varieties I, Invent. Math., 1, 287-354 (1966). | MR 204427 | Zbl 0219.14024

[M2] Mumford, D.: Tata lectures on Theta 2. Birkhäuser (1984). | MR 742776 | Zbl 0549.14014

[P] Perelomov, A.M.: Integrable systems of classical mechanics and Lie algebras I. Birkhäuser (1990). | MR 1048350 | Zbl 0699.70003

[S] Schlesinger, L., Uber eine Klasse von Differentialsystemen beliebiger Ordnung mit festen kritischen Punkten, J. für Math., 141, 96-145 (1912). | JFM 43.0385.01

[Sh] Shiota, T., The characterization of Jacobian varieties in terms of soliton equations, Invent.Math., 839, 333-382 (1986). | MR 818357 | Zbl 0621.35097

[V1] Vanhaecke, P., Linearizing two-dimensional integrable systems and the construction of action-angle variables, Math. Z., 211, 265-313 (1992). | MR 1184331 | Zbl 0758.58011

[V2] Vanhaecke, P., Stratifications of hyperelliptic Jacobians and the Sato Grassmannian. (MPI Preprint/93-24) (to appear in Acta Math. Appl.). | MR 1338445 | Zbl 0827.14015