The problem of deciding whether a graph manifold is finitely covered by a surface bundle over the circle is discussed in this paper.A necessary and sufficient condition in term of the solutions of a certain matrix equ...The problem of deciding whether a graph manifold is finitely covered by a surface bundle over the circle is discussed in this paper.A necessary and sufficient condition in term of the solutions of a certain matrix equation is obtained,as well as a necessary condition which is easy to compute. Our results sharpen and extend the earlier results of J.Leucke-Y.Wu,W.Neumann,and S.Wang-F. Yu in this topic.展开更多
A surface model called the fibre bundle model is proposed. This model represents a surface locally as a direct product of two curves： a base curve and a fibre curve. We introduce the fibre bundle model and then obtai...A surface model called the fibre bundle model is proposed. This model represents a surface locally as a direct product of two curves： a base curve and a fibre curve. We introduce the fibre bundle model and then obtain the Gaussian curvatures and the mean curvatures of a certain kind of fibre bundle surface models using 1-parameter groups of a linear Lie algebra as fibres. Some examples are given to verify our results.展开更多
We study weak approximation with Brauer-Manin obstruction with respect to extensions of number fields.For any nontrivial extension L/K,assuming a conjecture of M.Stoll,we prove that there exists a K-threefold satisfyi...We study weak approximation with Brauer-Manin obstruction with respect to extensions of number fields.For any nontrivial extension L/K,assuming a conjecture of M.Stoll,we prove that there exists a K-threefold satisfying weak approximation with Brauer-Manin obstruction off all archimedean places,while its base change to L fails.Then we illustrate this construction with an explicit unconditional example.展开更多
文摘The problem of deciding whether a graph manifold is finitely covered by a surface bundle over the circle is discussed in this paper.A necessary and sufficient condition in term of the solutions of a certain matrix equation is obtained,as well as a necessary condition which is easy to compute. Our results sharpen and extend the earlier results of J.Leucke-Y.Wu,W.Neumann,and S.Wang-F. Yu in this topic.
文摘A surface model called the fibre bundle model is proposed. This model represents a surface locally as a direct product of two curves： a base curve and a fibre curve. We introduce the fibre bundle model and then obtain the Gaussian curvatures and the mean curvatures of a certain kind of fibre bundle surface models using 1-parameter groups of a linear Lie algebra as fibres. Some examples are given to verify our results.
文摘We study weak approximation with Brauer-Manin obstruction with respect to extensions of number fields.For any nontrivial extension L/K,assuming a conjecture of M.Stoll,we prove that there exists a K-threefold satisfying weak approximation with Brauer-Manin obstruction off all archimedean places,while its base change to L fails.Then we illustrate this construction with an explicit unconditional example.
