Given any (2,4)-elliptic surface with nine smooth rational curves,eight (2)-curves and one (3)-curve,forming a Dynkin diagram of type [2,2][2,2][2,2][2,2,3],we show that a fake projective plane can be constructed from...Given any (2,4)-elliptic surface with nine smooth rational curves,eight (2)-curves and one (3)-curve,forming a Dynkin diagram of type [2,2][2,2][2,2][2,2,3],we show that a fake projective plane can be constructed from it by taking a degree 3 cover and then a degree 7 cover.We also determine the types of singular fibres of such a (2,4)-elliptic surface.展开更多
The linear stability of Lagrangian elliptic equilateral triangle homographic solutions in the classical planar three body problem depends on the mass parameter β = 27（m1m2 ＋ m2m3 ＋ m3m1）/（m1 ＋ m2 ＋ m3）2∈ [0,...The linear stability of Lagrangian elliptic equilateral triangle homographic solutions in the classical planar three body problem depends on the mass parameter β = 27（m1m2 ＋ m2m3 ＋ m3m1）/（m1 ＋ m2 ＋ m3）2∈ [0,9] and the eccentricity e ∈ [0,1）.In this paper we use Maslov-type index to study the stability of these solutions and prove that the elliptic Lagrangian solutions is hyperbolic for β ＆gt; 8 with any eccentricity.展开更多
基金supported by the National Research Foundation of Korea funded by the Ministry of Education,Science and Technology (Grant No. NRF-2007-2-C00002)
文摘Given any (2,4)-elliptic surface with nine smooth rational curves,eight (2)-curves and one (3)-curve,forming a Dynkin diagram of type [2,2][2,2][2,2][2,2,3],we show that a fake projective plane can be constructed from it by taking a degree 3 cover and then a degree 7 cover.We also determine the types of singular fibres of such a (2,4)-elliptic surface.
基金supported by National Natural Science Foundation of China (Grant No.11131004)
文摘The linear stability of Lagrangian elliptic equilateral triangle homographic solutions in the classical planar three body problem depends on the mass parameter β = 27（m1m2 ＋ m2m3 ＋ m3m1）/（m1 ＋ m2 ＋ m3）2∈ [0,9] and the eccentricity e ∈ [0,1）.In this paper we use Maslov-type index to study the stability of these solutions and prove that the elliptic Lagrangian solutions is hyperbolic for β ＆gt; 8 with any eccentricity.
