摘要
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.
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 the National Research Foundation of Korea funded by the Ministry of Education,Science and Technology (Grant No. NRF-2007-2-C00002)
