Research Article
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Year 2008, Volume: 1 Issue: 2, 15 - 32, 30.11.2008

Ahmed Lesfari

Abstract

References

  • [1] Abenda, S. and Fedorov, Yu., On the weak Kowalewski-Painleve Property for hyperelliptically separable systems, Acta Appl. Math., 60(2000) 137-178.
  • [2] Adler, M. and van Moerbeke, A., The complex geometry of the Kowalewski-Painleve analysis, Invent. Math., 97(1989) 3-51.
  • [3] Baker, S., Enolskii, V.Z. and Fordy, A.P., Integrable quartic potentials and coupled KdV equations, Phys. Lett., 201A(1995) 167-174.
  • [4] Belokolos, A.I., Bobenko, V.Z., Enol'skii, V.Z., Its, A.R. and Matveev. V.B., Algebro- Geometric approach to nonlinear integrable equations, Springer-Verlag 1994.
  • [5] Christiansen, P. L., Eilbeck, J. C., Enolskii, V. Z. and Kostov, N. A., Quasi-periodic and periodic solutions for coupled nonlinear Schrdinger equations of Manakov type, Proc. R. Soc., A 456(2000) 2263-2281.
  • [6] Conte, R., Musette, M. and Verhoeven, C., Completeness of the cubic and quartic Henon- Heiles hamiltonians, Theor. Math. Phys., 144(2005) 888-898.
  • [7] Eilbeck, J.C., Enolskii, V.Z., Kuznetsov, V.B. and Leykin, D.V., Linear r-matrix algebra for systems separable in parabolic coordinates, Phys. Lett., 180A(1993) 208-214.
  • [8] Grammaticos, B. Dorozzi, B., Ramani, A., Integrability of hamiltonians with third and fourth- degree polynomial potentials, J. Math. Phys., 24(1983) 2289-2295.
  • [9] Griffiths, P.A. and Harris, J., Principles of algebraic geometry, Wiley-Interscience 1978.
  • [10] Haine, L., Geodesic flow on SO(4) and Abelian surfaces. Math. Ann., 263(1983) 435-472.
  • [11] Hietarinta, J., Classical versus quantum integrability. J. Math. Phys., 25(1984) 1833-1840.
  • [12] Hietarinta, J., Direct methods for the search of the second invariant. Phys. Rep., 147(1987) 87-154.
  • [13] Kasperczuk, S., Integrability of the Yang-Mills hamiltonian system, Celes. Mech. and Dyn. Astr., 58(1994), 387-391. Erratum Celes. Mech. and Dyn. Astr., 60(1994), 289.
  • [14] Kostov, N.A., Quasi-periodical solutions of the integrable dynamical systems related to Hill's equation. Lett. Math. Phys., 17(1989) 95-104.
  • [15] Lesfari, A., Abelian surfaces and Kowalewski's top, Ann. Scient. Ecole Norm. Sup. Paris, 21(1988), sr. 4, 193-223.
  • [16] Lesfari., A., Completely integrable systems : Jacobi's heritage, J. Geom. Phys., 31(1999) 265-286.
  • [17] Lesfari, A., Le systeme differentiel de Henon-Heiles et les varietes Prym, Pacific J. Math., 212(2003), N1, 125-132.
  • [18] Lesfari, A., Le theoreme d'Arnold-Liouville et ses consequences, Elem. Math., 58 (2003) 6-20.
  • [19] Lesfari, A., Analyse des singularites de quelques systµemes integrables, C.R. Acad. Sci. Paris, 341(2005), Ser. I, 85-88.
  • [20] Lesfari, A., Abelian varieties, surfaces of general type and integrable systems, Beitrage Alge- bra Geom., 1(2007), Vol.48, 95-114.
  • [21] Lesfari, A., The Yang-Mills system and cyclic covering of abelian varieties, to appear Int. J. Geom. Methods Mod. Phys., Vol. 5(2008), N8.
  • [22] Moishezon., B.G., On n-dimensional compact varieties with n algebraically independent mero- morphic functions, Amer. Math. Soc. Transl., 63(1967), 51-177.
  • [23] Perelomov, A.M., Integrable system of classical mechanics and Lie algebras, Birkhauser 1994.
  • [24] Piovan, L., Cyclic coverings of abelian varieties and the Goryachev-Chaplygin top, Math. Ann., 294(1992), 755-764.
  • [25] Ravoson, V., Ramani, A. and Grammaticos, B., Generalized separability for a hamiltonian with nonseparable quartic potential, Phys. Lett., 191A(1994), 91-95.
  • [26] Tondo, G., On the integrability of stationary and restricted °ows of the KdV hierarchy, J. Phys. A : Mat. Gen., 28(1995), 5097-5115.
  • [27] Vanhaecke, P., Stratifications of hyperelliptic jacobians and the Sato Grassmannian, Acta Appl. Math., 40(1995), 143-172.
  • [28] Vanhaecke, P., Integrable systems and symmetric products of curves, Math. Z., 227(1998), 93-127.
  • [29] Verhoeven, C., Musette, M. and Conte, R., General solution of hamiltonians withs extend cubic and quartic potentials, Theor. Math. Phys., 134(2003), 128-138.
  • [30] Wojciechowski, S., Integrability of one particle in a perturbed central quartic potential, Physica Scripta, 31(1985), 433-438.

Affine parts of Abelian surfaces as complete intersection of three quartics

Year 2008, Volume: 1 Issue: 2, 15 - 32, 30.11.2008

Ahmed Lesfari

Abstract


Keywords

Abelian surfaces Curves Integrable systems Kummer surfaces

References

  • [1] Abenda, S. and Fedorov, Yu., On the weak Kowalewski-Painleve Property for hyperelliptically separable systems, Acta Appl. Math., 60(2000) 137-178.
  • [2] Adler, M. and van Moerbeke, A., The complex geometry of the Kowalewski-Painleve analysis, Invent. Math., 97(1989) 3-51.
  • [3] Baker, S., Enolskii, V.Z. and Fordy, A.P., Integrable quartic potentials and coupled KdV equations, Phys. Lett., 201A(1995) 167-174.
  • [4] Belokolos, A.I., Bobenko, V.Z., Enol'skii, V.Z., Its, A.R. and Matveev. V.B., Algebro- Geometric approach to nonlinear integrable equations, Springer-Verlag 1994.
  • [5] Christiansen, P. L., Eilbeck, J. C., Enolskii, V. Z. and Kostov, N. A., Quasi-periodic and periodic solutions for coupled nonlinear Schrdinger equations of Manakov type, Proc. R. Soc., A 456(2000) 2263-2281.
  • [6] Conte, R., Musette, M. and Verhoeven, C., Completeness of the cubic and quartic Henon- Heiles hamiltonians, Theor. Math. Phys., 144(2005) 888-898.
  • [7] Eilbeck, J.C., Enolskii, V.Z., Kuznetsov, V.B. and Leykin, D.V., Linear r-matrix algebra for systems separable in parabolic coordinates, Phys. Lett., 180A(1993) 208-214.
  • [8] Grammaticos, B. Dorozzi, B., Ramani, A., Integrability of hamiltonians with third and fourth- degree polynomial potentials, J. Math. Phys., 24(1983) 2289-2295.
  • [9] Griffiths, P.A. and Harris, J., Principles of algebraic geometry, Wiley-Interscience 1978.
  • [10] Haine, L., Geodesic flow on SO(4) and Abelian surfaces. Math. Ann., 263(1983) 435-472.
  • [11] Hietarinta, J., Classical versus quantum integrability. J. Math. Phys., 25(1984) 1833-1840.
  • [12] Hietarinta, J., Direct methods for the search of the second invariant. Phys. Rep., 147(1987) 87-154.
  • [13] Kasperczuk, S., Integrability of the Yang-Mills hamiltonian system, Celes. Mech. and Dyn. Astr., 58(1994), 387-391. Erratum Celes. Mech. and Dyn. Astr., 60(1994), 289.
  • [14] Kostov, N.A., Quasi-periodical solutions of the integrable dynamical systems related to Hill's equation. Lett. Math. Phys., 17(1989) 95-104.
  • [15] Lesfari, A., Abelian surfaces and Kowalewski's top, Ann. Scient. Ecole Norm. Sup. Paris, 21(1988), sr. 4, 193-223.
  • [16] Lesfari., A., Completely integrable systems : Jacobi's heritage, J. Geom. Phys., 31(1999) 265-286.
  • [17] Lesfari, A., Le systeme differentiel de Henon-Heiles et les varietes Prym, Pacific J. Math., 212(2003), N1, 125-132.
  • [18] Lesfari, A., Le theoreme d'Arnold-Liouville et ses consequences, Elem. Math., 58 (2003) 6-20.
  • [19] Lesfari, A., Analyse des singularites de quelques systµemes integrables, C.R. Acad. Sci. Paris, 341(2005), Ser. I, 85-88.
  • [20] Lesfari, A., Abelian varieties, surfaces of general type and integrable systems, Beitrage Alge- bra Geom., 1(2007), Vol.48, 95-114.
  • [21] Lesfari, A., The Yang-Mills system and cyclic covering of abelian varieties, to appear Int. J. Geom. Methods Mod. Phys., Vol. 5(2008), N8.
  • [22] Moishezon., B.G., On n-dimensional compact varieties with n algebraically independent mero- morphic functions, Amer. Math. Soc. Transl., 63(1967), 51-177.
  • [23] Perelomov, A.M., Integrable system of classical mechanics and Lie algebras, Birkhauser 1994.
  • [24] Piovan, L., Cyclic coverings of abelian varieties and the Goryachev-Chaplygin top, Math. Ann., 294(1992), 755-764.
  • [25] Ravoson, V., Ramani, A. and Grammaticos, B., Generalized separability for a hamiltonian with nonseparable quartic potential, Phys. Lett., 191A(1994), 91-95.
  • [26] Tondo, G., On the integrability of stationary and restricted °ows of the KdV hierarchy, J. Phys. A : Mat. Gen., 28(1995), 5097-5115.
  • [27] Vanhaecke, P., Stratifications of hyperelliptic jacobians and the Sato Grassmannian, Acta Appl. Math., 40(1995), 143-172.
  • [28] Vanhaecke, P., Integrable systems and symmetric products of curves, Math. Z., 227(1998), 93-127.
  • [29] Verhoeven, C., Musette, M. and Conte, R., General solution of hamiltonians withs extend cubic and quartic potentials, Theor. Math. Phys., 134(2003), 128-138.
  • [30] Wojciechowski, S., Integrability of one particle in a perturbed central quartic potential, Physica Scripta, 31(1985), 433-438.
There are 30 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Ahmed Lesfari This is me

Publication Date November 30, 2008
Published in Issue Year 2008 Volume: 1 Issue: 2

Cite

APA Lesfari, A. (2008). Affine parts of Abelian surfaces as complete intersection of three quartics. International Electronic Journal of Geometry, 1(2), 15-32.
AMA Lesfari A. Affine parts of Abelian surfaces as complete intersection of three quartics. Int. Electron. J. Geom. November 2008;1(2):15-32.
Chicago Lesfari, Ahmed. “Affine Parts of Abelian Surfaces As Complete Intersection of Three Quartics”. International Electronic Journal of Geometry 1, no. 2 (November 2008): 15-32.
EndNote Lesfari A (November 1, 2008) Affine parts of Abelian surfaces as complete intersection of three quartics. International Electronic Journal of Geometry 1 2 15–32.
IEEE A. Lesfari, “Affine parts of Abelian surfaces as complete intersection of three quartics”, Int. Electron. J. Geom., vol. 1, no. 2, pp. 15–32, 2008.
ISNAD Lesfari, Ahmed. “Affine Parts of Abelian Surfaces As Complete Intersection of Three Quartics”. International Electronic Journal of Geometry 1/2 (November 2008), 15-32.
JAMA Lesfari A. Affine parts of Abelian surfaces as complete intersection of three quartics. Int. Electron. J. Geom. 2008;1:15–32.
MLA Lesfari, Ahmed. “Affine Parts of Abelian Surfaces As Complete Intersection of Three Quartics”. International Electronic Journal of Geometry, vol. 1, no. 2, 2008, pp. 15-32.
Vancouver Lesfari A. Affine parts of Abelian surfaces as complete intersection of three quartics. Int. Electron. J. Geom. 2008;1(2):15-32.