Integrable systems and projective images of Kummer surfaces
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 29 (2000) no. 2, p. 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},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 29},
     number = {2},
     year = {2000},
     pages = {351-392},
     zbl = {0980.14027},
     mrnumber = {1784179},
     language = {en},
     url = {http://www.numdam.org/item/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, Série 4, Tome 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 758421 | Zbl 0545.58027

[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 912838 | Zbl 0607.14030

[3] M. Adler - P. Van Moerbeke, The complex geometry of the Kowalewski-Painlevé analysis, Invent. Math. 97 (1989), 3-51. | MR 999312 | Zbl 0678.58020

[4] W. Barth, Affine parts of Abelian surfaces as complete intersections of four quadrics, Math. Ann. 278 (1987), 117-131. | MR 909220 | Zbl 0675.14023

[5] W. Barth - C. Peters - A. Van De Ven, A., "Compacts Complex Surfaces", Springer-Verlag, 1984. | MR 749574 | Zbl 0718.14023

[6] T. Bauer, Projective images of Kummer surfaces, Math. Ann. 299 (1994), 155-170. | MR 1273081 | Zbl 0793.14029

[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 1125667 | Zbl 0756.14017

[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 732439 | Zbl 0849.14014

[9] J. Bertin - P. Vanhaecke, The even master system and generalized Kummer surfaces, Math. Proc. Cambridge Philos. Soc. 116 (1994), 131-142. | MR 1274163 | Zbl 0828.14022

[10] P. Griffiths - J. Harris, J., "Principles of Algebraic Geometry ", Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York, 1978. | MR 507725 | Zbl 0408.14001

[11] R. Hartshorne, "Algebraic Geometry", Springer-Verlag, New York, 1977, Graduate Texts in Mathematics, No. 52. | MR 463157 | Zbl 0367.14001

[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 1097176 | Zbl 0716.14025

[13] J. Huebschmann, Poisson structures on certain moduli spaces for bundles on a surface, Ann. Inst. Fourier (Grenoble) 45 (1995), 65-91. | Numdam | MR 1324125 | Zbl 0819.58010

[14] C.M. Jessop, "A Treatise on the Line Complex", Chelsea Publishing Co., New York, 1969. | MR 247995 | Zbl 0209.25001

[15] K. Kodaira, On compact complex analytic surfaces. I, Ann. of Math. (2) 71 (1960), 111-152. | MR 132556 | Zbl 0098.13004

[16] H. Lange - C. Birkenhake, "Complex Abelian Varieties", Grund. der Math. Wiss., vol. 302, Springer-Verlag, Berlin, 1992. | MR 1217487 | Zbl 0779.14012

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

[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 742776 | Zbl 0549.14014

[19] D. Mumford, "Abelian Varieties", Tata Institute of Fundamental Research Studies in Mathematics, vol. 5, Oxford University Press Oxford, 1985. | MR 282985 | Zbl 0583.14015

[20] M.S. Narasimhan - S. Ramanan, Moduli of vector bundles on a compact Riemann surface, Ann. of Math. (2) 89 (1969), 14-51. | MR 242185 | Zbl 0186.54902

[21] L. Piovan, L., Algebraically completely integrable systems and Kummer varieties, Math. Ann. 290 (1991), no. 2, 349-403. | MR 1109639 | Zbl 0743.58021

[22] C.P. Ramanujam, Remarks on the Kodaira vanishing theorem, J. Indian Math. Soc. (N.S.) 36 (1972), 41-51. | MR 330164 | Zbl 0276.32018

[23] M.J. Remy, Sur une famille dénombrable de surfaces hyperelliptiques du quatrième ordre, Bull. Soc. Math. France 35 (1907), 53-69. | JFM 38.0661.03 | Numdam | MR 1504565

[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 364263 | Zbl 0301.14011

[26] I.R. Shafarevich, "Algebraic Surfaces", American Mathematical Society, 1967, Proceedings of the Steklov Institute of Mathematics, no. 75, 1965. | MR 215850

[27] T. Szemberg, Intersection of Quadrics in P5, Kummer surfaces and their moduli, Friedrich-Alexander-Universität Erlangen- Nürnberg, 1994. | Zbl 0876.14025

[28] P. Vanhaecke, "Integrable Systems in the Realm of Algebraic Geometry", Lecture Notes in Mathematics, vol. 1638, Springer-Verlag Berlin, 1996. | MR 1601824 | Zbl 0867.58039