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The Intersection of 4 Quadrics in P6, Abelian Surfaces and Their Moduli

Bibliographic reference Adler, M. ; Van Moerbeke, Pierre. The Intersection of 4 Quadrics in P6, Abelian Surfaces and Their Moduli. In: Mathematische Annalen, Vol. 279, no. 1, p. 25-85 (1987)
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  1. Adler, M., van Moerbeke, P.: The algebraic integrability of geodesic flow onSO(4). Invent. Math.67, 297?326 (1982) with an appendix by D. Mumford
  2. Adler, M., van Moerbeke, P.: Geodesic flow onSO(4) and the intersection of quadrics. Proc. Natl. Acad. Sci. USA81, 4613?4616 (1984)
  3. Adler, M., van Moerbeke, P.: A new geodesic flow onSO(4). Probability, Statistical mechanics, and Number theory Adv. Math. Suppl. Stud. dedicated to Mark Kac, edited by G.C. Rota, 9. New York, London: Acad. Press 1986
  4. Adler, M., van Moerbeke, P.: A full classification of algebraically completely integrable geodesic flows onSO(4). Preprint (1987)
  5. Adler, M., van Moerbeke, P.: A systematic approach towards solving integrable systems. In: Perspectives in mathematics. London, New York: Academic Press 1986
  6. Arnold, V.I.: Mathematical methods of classical mechanics. Berlin, Heidelberg, New York: Springer 1978
  7. Barth, W.: Abelian surfaces with (1,2)-polarization. Conf. on Alg. Geom., Sendai, 1985
  8. Barth, W.: Moduli of vector bundles on the projective planes. Invent. Math.42, 63?91 (1977)
  9. Griffiths, P., Harris, J.: Principles of algebraic geometry. New York: Wiley 1978
  10. Haine, L., Geodesic flow onSO(4) and abelian surfaces. Math. Ann.263, 435?472 (1983)
  11. Jacobi, C.G.J.: Vorlesungen �ber Dynamik. K�nigsberg 1866 Gesammelte Werke Supplementband. Berlin: Teubner 1884
  12. Klein, F.: Elementar Mathematik vom h�heren Standpunkt aus. 4th ed., Berlin: Springer 1933 Vol. 1, pl. 3, Trigonometrie, pp. 184?201
  13. Kn�rrer, H.: Geodesics on the ellipsoid. Invent. Math.59, 119?144 (1980)
  14. K�tter, F.: �ber die Bewegung eines festen K�rpers in einer Fl�ssigkeit. I, II. J. Reine Angew. Math.109, 51?81, 89?111 (1892)
  15. K�tter, F.: Die von Steklov und Lyapunov entdeckten integralen F�lle der Bewegung eines K�rpers in einer Fl�ssigkeit. Sitzungsber. K�nigl. Preuss. Akad. Wiss. Berlin6, 79?87 (1900)
  16. van Moerbeke, P.: Algebraic complete integrability of Hamiltonian systems and Kac-Moody lie algebras. Proc. Int. Congr. of Math., Warszawa, August 1983
  17. van Moerbeke, P.: Algebraic geometrical methods in Hamiltonian mechanics. (Royal Society Meeting, November 1984). Philos. Trans. R. Soc. Lond. A315, 379?390 (1985)
  18. Moser, J.: Geometry of quadrics and spectral theory, 147?188. The Chern Symposium 1979. Berlin, Heidelberg, New York: Springer 1979
  19. Mumford, D.: Appendix to [1], Invent. Math.67, 247?331 (1982)
  20. Perelomov, A.M.: Some remarks on the integrability of the equations of motion of a rigid body in an ideal fluid. Funct. Anal. Appl.15, 83?85 (1981), transl. 144?146
  21. Reid, M.: The complete intersection of two or more quadrics. Ph. D. dissertation (Cambridge University), 1972
  22. Tyurin, A.: On intersections of quadrics. Russ. Math. Surv.30, 51?105 (1975)
  23. Adler, M., van Moerbeke, P.: Realizing the Kowalewski top and the Henon-Heiles system as a Manakov geodesic flow onSO(4) and a family of Lax pairs. Commun. Math. Phys. (1987), to appear
  24. Barth, W.: Affine abelian surfaces as complete intersections of four quadrics. Math. Ann. (1987) to appear
  25. Horozov, E., van Moerbeke, P.: Abelian surfaces of polarization (1,2) and Kowalewski's top. Commun. Pure Appl. Math. (1988) (to appear)