A special case of the Garnier system, ( 1 , 4 ) -polarized abelian surfaces and their moduli

Pol Vanhaecke

Compositio Mathematica (1994)

  • Volume: 92, Issue: 2, page 157-203
  • ISSN: 0010-437X

How to cite

top

Vanhaecke, Pol. "A special case of the Garnier system, $(1, 4)$-polarized abelian surfaces and their moduli." Compositio Mathematica 92.2 (1994): 157-203. <http://eudml.org/doc/90303>.

@article{Vanhaecke1994,
author = {Vanhaecke, Pol},
journal = {Compositio Mathematica},
keywords = {abelian surfaces of type (1,4); integrable systems},
language = {eng},
number = {2},
pages = {157-203},
publisher = {Kluwer Academic Publishers},
title = {A special case of the Garnier system, $(1, 4)$-polarized abelian surfaces and their moduli},
url = {http://eudml.org/doc/90303},
volume = {92},
year = {1994},
}

TY - JOUR
AU - Vanhaecke, Pol
TI - A special case of the Garnier system, $(1, 4)$-polarized abelian surfaces and their moduli
JO - Compositio Mathematica
PY - 1994
PB - Kluwer Academic Publishers
VL - 92
IS - 2
SP - 157
EP - 203
LA - eng
KW - abelian surfaces of type (1,4); integrable systems
UR - http://eudml.org/doc/90303
ER -

References

top
  1. [A] Arnold, V.: Mathematical Methods of Classical Mechanics. Springer-Verlag (1978). Zbl0386.70001MR690288
  2. [AvM1] Adler, M., van Moerbeke, P.: Algebraic completely integrable systems: a systematic approach. Perspectives in Mathematics, Academic Press (to appear in 1995). 
  3. [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). Zbl0647.58022
  4. [AvM3] Adler, M., van Moerbeke, P., The complex geometry of the Kowalewski-Painlevé analysis, Invent. Math., 97, 3-51 (1987). Zbl0678.58020MR999312
  5. [B] Baltuch, J.: Integrable systems and reducible Abelian surfaces of type (1,2). Doctoral thesis at Brandeis University, 1991. 
  6. [Ba] Barth, W.: Abelian surfaces with (1, 2) polarization, Conference on Algebraic Geometry, Sendai (1985). Zbl0639.14023
  7. [Be] Beauville, A., Jacobiennes des courbes spectrales et systèmes hamiltoniens complètement intégrables, Acta Math., 164, 211-235 (1990). Zbl0712.58031MR1049157
  8. [BLS] Birkenhake, C., Lange, H., van Straten, D., Abelian surfaces of type (1,4), Math. Ann., 285, 625-646 (1989). Zbl0714.14028MR1027763
  9. [Bu] Bueken, P.: A geodesic flow on SO(4) and Abelian surfaces of type (1, 4). (Preprint). 
  10. [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). MR497773
  11. [D] Dubrovin, B.A., Theta functions and nonlinear equations, Russian Math. Surveys, 36/2, 11-92 (1982). Zbl0549.58038MR616797
  12. [F] Flaschka, H., Monodromy- and Spectrum-Preserving Deformations I, Commun. Math. Phys., 76, 65-116 (1980). Zbl0439.34005MR588248
  13. [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). Zbl47.0404.01JFM47.0404.01
  14. [Gr] Griffiths, P.A., Linearizing flows and a cohomological interpretation of Lax equations, Am. J. of Math., 107, 1445-1483 (1985). Zbl0585.58028MR815768
  15. [GH] Griffiths, P. and Harris, J.: Principles of Algebraic Geometry. Wiley-Interscience, New York (1978). Zbl0408.14001MR507725
  16. [Hu] Hudson, R.W.H.: Kummer's quartic surface. Cambridge: Cambridge University Press (1990); first published in 1905. Zbl0716.14025MR1097176JFM36.0709.03
  17. [LB] Lange, H., Birkenhake, C.: Complex Abelian Varieties. Springer-Verlag (1992). Zbl0779.14012MR1217487
  18. [M1] Mumford, D., On the equations defining Abelian varieties I, Invent. Math., 1, 287-354 (1966). Zbl0219.14024MR204427
  19. [M2] Mumford, D.: Tata lectures on Theta 2. Birkhäuser (1984). Zbl0549.14014MR742776
  20. [P] Perelomov, A.M.: Integrable systems of classical mechanics and Lie algebras I. Birkhäuser (1990). Zbl0699.70003MR1048350
  21. [S] Schlesinger, L., Uber eine Klasse von Differentialsystemen beliebiger Ordnung mit festen kritischen Punkten, J. für Math., 141, 96-145 (1912). Zbl43.0385.01JFM43.0385.01
  22. [Sh] Shiota, T., The characterization of Jacobian varieties in terms of soliton equations, Invent.Math., 839, 333-382 (1986). Zbl0621.35097MR818357
  23. [V1] Vanhaecke, P., Linearizing two-dimensional integrable systems and the construction of action-angle variables, Math. Z., 211, 265-313 (1992). Zbl0758.58011MR1184331
  24. [V2] Vanhaecke, P., Stratifications of hyperelliptic Jacobians and the Sato Grassmannian. (MPI Preprint/93-24) (to appear in Acta Math. Appl.). Zbl0827.14015MR1338445

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.