  We give a geometric proof that Hasse principle holds for the following
varieties defined over global function fields: smooth quadric hypersurfaces in
odd characteristic, smooth cubic hypersurfaces of dimension at least $4$ in
characteristic at least $7$, and smooth complete intersections of two quadrics
of dimension at least $3$ in odd characteristics.
  In Appendix A we explain how to modify a previous argument of the author to
prove weak approximation for cubic hypersurfaces defined over function fields
of curves over algebraically closed fields of characteristic at least $7$. In
Appendix B we prove some corollaries of Koll\'ar's results on the fundamental
group of separably rationally connected varieties.
