Integrable systems and projective images of Kummer surfaces
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 29 (2000) no. 2, pp. 351-392.
@article{ASNSP_2000_4_29_2_351_0,
     author = {Piovan, Luis A. and Vanhaecke, Pol},
     title = {Integrable systems and projective images of {Kummer} surfaces},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {351--392},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 29},
     number = {2},
     year = {2000},
     zbl = {0980.14027},
     mrnumber = {1784179},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2000_4_29_2_351_0/}
}
TY  - JOUR
AU  - Piovan, Luis A.
AU  - Vanhaecke, Pol
TI  - Integrable systems and projective images of Kummer surfaces
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 2000
DA  - 2000///
SP  - 351
EP  - 392
VL  - Ser. 4, 29
IS  - 2
PB  - Scuola normale superiore
UR  - http://www.numdam.org/item/ASNSP_2000_4_29_2_351_0/
UR  - https://zbmath.org/?q=an%3A0980.14027
UR  - https://www.ams.org/mathscinet-getitem?mr=1784179
LA  - en
ID  - ASNSP_2000_4_29_2_351_0
ER  - 
%0 Journal Article
%A Piovan, Luis A.
%A Vanhaecke, Pol
%T Integrable systems and projective images of Kummer surfaces
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 2000
%P 351-392
%V Ser. 4, 29
%N 2
%I Scuola normale superiore
%G en
%F ASNSP_2000_4_29_2_351_0
Piovan, Luis A.; Vanhaecke, Pol. Integrable systems and projective images of Kummer surfaces. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 29 (2000) no. 2, pp. 351-392. http://www.numdam.org/item/ASNSP_2000_4_29_2_351_0/

[1] M. Adler - P. Van Moerbeke, Geodesic flow on SO(4) and the intersection of quadrics, Proc. Nat. Acad. Sci. U.S.A. 81 (1984), Phys. Sci., 4613-4616. | MR | Zbl

[2] M. Adler - P. Van Moerbeke, The intersection of four quadrics in P6, Abelian surfaces and their moduli, Math. Ann. 279 (1987), 25-85. | MR | Zbl

[3] M. Adler - P. Van Moerbeke, The complex geometry of the Kowalewski-Painlevé analysis, Invent. Math. 97 (1989), 3-51. | MR | Zbl

[4] W. Barth, Affine parts of Abelian surfaces as complete intersections of four quadrics, Math. Ann. 278 (1987), 117-131. | MR | Zbl

[5] W. Barth - C. Peters - A. Van De Ven, A., "Compacts Complex Surfaces", Springer-Verlag, 1984. | MR | Zbl

[6] T. Bauer, Projective images of Kummer surfaces, Math. Ann. 299 (1994), 155-170. | MR | Zbl

[7] A. Beauville, Fibrés de rang deux sur une courbe, fibré déterminant et fonctions thêta. II, Bull. Soc. Math. France 119 (1991), 259-291. | Numdam | MR | Zbl

[8] A. Beauville, A., "Complex Algebraic Surfaces", Second ed., London Mathematical Society Student Texts vol. 34, Cambridge University Press, Cambridge, 1996, Translated from the 1978 French original by R. Barlow, with assistance from N.I. Shepherd-Barron and M. Reid. | MR | Zbl

[9] J. Bertin - P. Vanhaecke, The even master system and generalized Kummer surfaces, Math. Proc. Cambridge Philos. Soc. 116 (1994), 131-142. | MR | Zbl

[10] P. Griffiths - J. Harris, J., "Principles of Algebraic Geometry ", Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York, 1978. | MR | Zbl

[11] R. Hartshorne, "Algebraic Geometry", Springer-Verlag, New York, 1977, Graduate Texts in Mathematics, No. 52. | MR | Zbl

[12] R.W.H.T. Hudson, "Kummer's Quartic Surface", Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1990, With a foreword by W. Barth, Revised reprint of the 1905 original. | MR | Zbl

[13] J. Huebschmann, Poisson structures on certain moduli spaces for bundles on a surface, Ann. Inst. Fourier (Grenoble) 45 (1995), 65-91. | Numdam | MR | Zbl

[14] C.M. Jessop, "A Treatise on the Line Complex", Chelsea Publishing Co., New York, 1969. | MR | Zbl

[15] K. Kodaira, On compact complex analytic surfaces. I, Ann. of Math. (2) 71 (1960), 111-152. | MR | Zbl

[16] H. Lange - C. Birkenhake, "Complex Abelian Varieties", Grund. der Math. Wiss., vol. 302, Springer-Verlag, Berlin, 1992. | MR | Zbl

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

[18] D. Mumford, "Tata Lectures on Theta. II", Progress in Mathematics, vol. 43, Birkhäuser Boston Inc., Boston, MA, 1984, Jacobian theta functions and differential equations, With the collaboration of C. Musili, M. Nori, E. Previato, M. Stillman and H. Umemura. | MR | Zbl

[19] D. Mumford, "Abelian Varieties", Tata Institute of Fundamental Research Studies in Mathematics, vol. 5, Oxford University Press Oxford, 1985. | MR | Zbl

[20] M.S. Narasimhan - S. Ramanan, Moduli of vector bundles on a compact Riemann surface, Ann. of Math. (2) 89 (1969), 14-51. | MR | Zbl

[21] L. Piovan, L., Algebraically completely integrable systems and Kummer varieties, Math. Ann. 290 (1991), no. 2, 349-403. | MR | Zbl

[22] C.P. Ramanujam, Remarks on the Kodaira vanishing theorem, J. Indian Math. Soc. (N.S.) 36 (1972), 41-51. | MR | Zbl

[23] M.J. Remy, Sur une famille dénombrable de surfaces hyperelliptiques du quatrième ordre, Bull. Soc. Math. France 35 (1907), 53-69. | JFM | Numdam | MR

[24] J.E. Rosenberg, Hessian quartic surfaces that are Kummer surfaces, math. AG/9903037.

[25] B. Saint-Donat, B., Projective models of K - 3 surfaces, Amer. J. Math. 96 (1974), 602-639. | MR | Zbl

[26] I.R. Shafarevich, "Algebraic Surfaces", American Mathematical Society, 1967, Proceedings of the Steklov Institute of Mathematics, no. 75, 1965. | MR

[27] T. Szemberg, Intersection of Quadrics in P5, Kummer surfaces and their moduli, Friedrich-Alexander-Universität Erlangen- Nürnberg, 1994. | Zbl

[28] P. Vanhaecke, "Integrable Systems in the Realm of Algebraic Geometry", Lecture Notes in Mathematics, vol. 1638, Springer-Verlag Berlin, 1996. | MR | Zbl