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

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

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.

Details

Primary Language English
Journal Section Research Article
Authors

Ahmed LESFARİ This is me

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

Cite

Bibtex @research article { iejg581787, journal = {International Electronic Journal of Geometry}, eissn = {1307-5624}, address = {}, publisher = {Kazım İLARSLAN}, year = {2008}, volume = {1}, number = {2}, pages = {15 - 32}, title = {Affine parts of Abelian surfaces as complete intersection of three quartics}, key = {cite}, author = {Lesfari, Ahmed} }
APA Lesfari, A. (2008). Affine parts of Abelian surfaces as complete intersection of three quartics . International Electronic Journal of Geometry , 1 (2) , 15-32 . Retrieved from https://dergipark.org.tr/en/pub/iejg/issue/46296/581787
MLA Lesfari, A. "Affine parts of Abelian surfaces as complete intersection of three quartics" . International Electronic Journal of Geometry 1 (2008 ): 15-32 <https://dergipark.org.tr/en/pub/iejg/issue/46296/581787>
Chicago Lesfari, A. "Affine parts of Abelian surfaces as complete intersection of three quartics". International Electronic Journal of Geometry 1 (2008 ): 15-32
RIS TY - JOUR T1 - Affine parts of Abelian surfaces as complete intersection of three quartics AU - AhmedLesfari Y1 - 2008 PY - 2008 N1 - DO - T2 - International Electronic Journal of Geometry JF - Journal JO - JOR SP - 15 EP - 32 VL - 1 IS - 2 SN - -1307-5624 M3 - UR - Y2 - 2022 ER -
EndNote %0 International Electronic Journal of Geometry Affine parts of Abelian surfaces as complete intersection of three quartics %A Ahmed Lesfari %T Affine parts of Abelian surfaces as complete intersection of three quartics %D 2008 %J International Electronic Journal of Geometry %P -1307-5624 %V 1 %N 2 %R %U
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 .
AMA Lesfari A. Affine parts of Abelian surfaces as complete intersection of three quartics. Int. Electron. J. Geom.. 2008; 1(2): 15-32.
Vancouver Lesfari A. Affine parts of Abelian surfaces as complete intersection of three quartics. International Electronic Journal of Geometry. 2008; 1(2): 15-32.
IEEE A. Lesfari , "Affine parts of Abelian surfaces as complete intersection of three quartics", International Electronic Journal of Geometry, vol. 1, no. 2, pp. 15-32, Nov. 2008